Quantum Space Technologies
Jakub Mielczarek
Photons - quanta of light
Horizontal polarization
Vertical polarization
CC BY-3.0
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|V i = |1i<latexit sha1_base64="z0F4Em0l+qSkDByc8LczO63xTyE=">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</latexit><latexit sha1_base64="z0F4Em0l+qSkDByc8LczO63xTyE=">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</latexit><latexit sha1_base64="z0F4Em0l+qSkDByc8LczO63xTyE=">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</latexit><latexit sha1_base64="kOaz2q6ekYexSM32zcee3Fh71WA=">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</latexit>
state
state
| i = cos(✓/2)|0i + ei
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sha1_base64="/RKKLTVSQdlFkB/lm43n5vKj+mI=">AAADEHicjVHNTtwwGBzSQoHys7THXqyukEBIS7KX9oKE2gtSL1uJBSQCyDFm1yKbRLZTCe3yEn2T3rghrn0B1Ft7g7fgszFqASHqKMl4vpmxPzurcmVsHP8ai168HJ94NTk1/Xpmdm6+sfBmy5S1FrIryrzUOxk3MleF7Fplc7lTackHWS63s+PPrr79TWqjymLTnlRyb8B7hTpSgluiDhpfRiztGMVSzYteLtkaS0VpllLbl5avtpfZKA6lFbk/VGnVV6csNar4KxklQXHQaMat2A/2GCQBNBFGp2xcIsUhSgjUGECigCWcg8PQs4sEMSri9jAkThNSvi5ximny1qSSpODEHtO3R7PdwBY0d5nGuwWtktOrycmwSJ6SdJqwW435eu2THftU9tBnur2d0D8LWQNiLfrEPue7U/6vz/VicYSPvgdFPVWecd2JkFL7U3E7Z/90ZSmhIs7hQ6prwsI7786ZeY/xvbuz5b5+5ZWOdXMRtDWu3S7pgpOH1/kYbLVbSdxKvrab65/CVU/iHd5jie7zA9axgQ66lP0Dl/iNP9H36Cw6jy5updFY8LzFvRH9vAEvAaxs</latexit>
In general, photon is in quantum superposition of the
two polarizations:
Quantum state of a photon is
an example of a qubit (quantum bit).
CC BY-SA 3.0
Photon Qubit
This is due to the fact that photon
is a masless spin 1 particle with
two helicity states:
|Li =
1
p
2
(|0i i|1i)
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|Ri =
1
p
2
(|0i + i|1i)
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v
v
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ˆX, ˆY , ˆZ<latexit sha1_base64="bQjmKtIZYRpHF0PdPMfkLPKbY7g=">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</latexit><latexit sha1_base64="bQjmKtIZYRpHF0PdPMfkLPKbY7g=">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</latexit><latexit sha1_base64="bQjmKtIZYRpHF0PdPMfkLPKbY7g=">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</latexit><latexit sha1_base64="Eg2mlhG2CrbZkoB5Uo5rBRx4yXk=">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</latexit>
Pauli operators
ˆX|+i = |+i<latexit sha1_base64="bSg3Ak1F8cmqe+ogCu0LvvwChbY=">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</latexit><latexit sha1_base64="bSg3Ak1F8cmqe+ogCu0LvvwChbY=">AAAC5nicjVHLSsNAFD3GV62vqks3o0UQhJKIoBuh6MZlBfuAVsokjm0wTcJkIpTatTt34tYfcKufIv6B/oV3xhR8IDohybnn3nNm7lw3DvxE2fbLmDU+MTk1nZvJz87NLywWlpZrSZRKT1S9KIhkw+WJCPxQVJWvAtGIpeA9NxB19+JQ5+uXQiZ+FJ6ofixOe7wT+ue+xxVR7cJaq8vVoDFkV2yLtSQPO4Fg+5+jdqFol2yz2E/gZKCIbFWiwjNaOEMEDyl6EAihCAfgSOhpwoGNmLhTDIiThHyTFxgiT9qUqgRVcGIv6NuhqJmxIcXaMzFqj3YJ6JWkZNggTUR1krDejZl8apw1+5v3wHjqs/Xp72ZePWIVusT+pRtV/lene1E4x57pwaeeYsPo7rzMJTW3ok/OPnWlyCEmTuMzykvCnlGO7pkZTWJ613fLTf7VVGpWx15Wm+JNn5IG7Hwf509Q2y45dsk53imWD7JR57CKdWzSPHdRxhEqqJL3NR7wiCera91Yt9bdR6k1lmlW8GVZ9+9uFJt0</latexit><latexit sha1_base64="bSg3Ak1F8cmqe+ogCu0LvvwChbY=">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</latexit><latexit sha1_base64="dkPeDTKxAFfjzdikIollt54d5LU=">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</latexit>
ˆX| i = | i<latexit sha1_base64="R0Iw/b772D2LTIh+R+W5InbgksM=">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</latexit><latexit sha1_base64="R0Iw/b772D2LTIh+R+W5InbgksM=">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</latexit><latexit sha1_base64="R0Iw/b772D2LTIh+R+W5InbgksM=">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</latexit><latexit sha1_base64="e47ciWWNaX/7zQfcvJ4DhxPktZI=">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</latexit>
ˆY |Ri = |Ri<latexit sha1_base64="StHI+xit9FBfHz25gVga3DpSzXc=">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</latexit><latexit sha1_base64="StHI+xit9FBfHz25gVga3DpSzXc=">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</latexit><latexit sha1_base64="StHI+xit9FBfHz25gVga3DpSzXc=">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</latexit><latexit sha1_base64="svXI3Aa5lwJ4fNh+f2uJer/aBVg=">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</latexit>
ˆY |Li = |Li<latexit sha1_base64="DVSKc7mOwq7KZ4hohkvPqFtldR8=">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</latexit><latexit sha1_base64="DVSKc7mOwq7KZ4hohkvPqFtldR8=">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</latexit><latexit sha1_base64="DVSKc7mOwq7KZ4hohkvPqFtldR8=">AAAC6HicjVHLSsNAFD3GV62vqks3g0VwY0lE0I1QdOPCRQX7kLbIJI41Nk3CZCJI9QPcuRO3/oBb/RLxD/QvvDNGqIrohCT3nnvOmblz3TjwE2XbL0PW8Mjo2HhuIj85NT0zW5ibryVRKj1R9aIgkg2XJyLwQ1FVvgpEI5aC99xA1N3ujq7Xz4VM/Cg8UBexaPd4J/RPfI8rgo4KxdYpV/3DK3bJ9lhL8rATCLbFVgdTYtkl2yz2M3CyoIhsVaLCM1o4RgQPKXoQCKEoDsCR0NOEAxsxYW30CZMU+aYucIU8aVNiCWJwQrv07VDWzNCQcu2ZGLVHuwT0SlIyLJMmIp6kWO/GTD01zhr9zbtvPPXZLujvZl49QhVOCf1L98n8r073onCCTdODTz3FBtHdeZlLam5Fn5wNdKXIISZMx8dUlxR7Rvl5z8xoEtO7vltu6q+GqVGdexk3xZs+JQ3Y+T7On0FtreTYJWd/vVjezkadwyKWsELz3EAZu6igSt7XeMAjnqwz68a6te4+qNZQplnAl2XdvwMpLJwY</latexit><latexit sha1_base64="sxa3wwQKzQXoOO2F6wlEr5ePj2I=">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</latexit>
|+i =
1
p
2
(|0i + |1i)
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| i =
1
p
2
(|0i |1i)
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Quantum key distribution - QKD
No-cloning theorem - an unknown state can’t be copied.
Distrobution of private key utilizing quantum bits and
fundamental properties of quantum mechanics:
Measusrement reduce a quantum state.
Mehic, M., Maurhart, O., Rass, S. et al. Quantum Inf Process (2017) 16: 253
No-cloning of qubits
| i = ↵|0i + |1i<latexit sha1_base64="KnjSa2qv+IpETeXL6+1Kh1Ctio4=">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</latexit><latexit sha1_base64="KnjSa2qv+IpETeXL6+1Kh1Ctio4=">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</latexit><latexit sha1_base64="KnjSa2qv+IpETeXL6+1Kh1Ctio4=">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</latexit><latexit sha1_base64="PURkbTB2QPwPjzeIWLcco5jcik8=">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</latexit>
We would like to copy an unknown state
ˆC(| i ⌦ | i) = | i ⌦ | i<latexit sha1_base64="MBnsbeGh+PaIk5YNi+Fyxiqy1v0=">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</latexit><latexit 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sha1_base64="MBnsbeGh+PaIk5YNi+Fyxiqy1v0=">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</latexit><latexit 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A copying operator has to satisfy:
ˆC(|0i ⌦ | i) = |0i ⌦ |0i<latexit sha1_base64="CVZYbJL/WOz+KKsp+t2TXR2jkWM=">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</latexit><latexit sha1_base64="CVZYbJL/WOz+KKsp+t2TXR2jkWM=">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</latexit><latexit sha1_base64="CVZYbJL/WOz+KKsp+t2TXR2jkWM=">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</latexit><latexit sha1_base64="XSUYELRRaosTU5WWGMt3lWnoTQg=">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</latexit>
ˆC(|1i ⌦ | i) = |1i ⌦ |1i<latexit sha1_base64="M5B+B1V26f4JSp9qkb28/DRUnRs=">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</latexit><latexit sha1_base64="M5B+B1V26f4JSp9qkb28/DRUnRs=">AAADC3icjVHLSsQwFD3W9/gademmOAi6GVoRdCOIgrgcwRkFK5LWOBPsizQVZMZP8E/cuRO3/oAbEf0A/QtvYkfUQTSl7cm555zkJn4aikw5zlOf1T8wODQ8MloaG5+YnCpPzzSyJJcBrwdJmMgDn2U8FDGvK6FCfpBKziI/5Pv+2Zau759zmYkk3lMXKT+KWDMWpyJgiqjj8rbXYqq9dbnYcW1PsrgZcttLlIh4Zne8Wkt02aX1jtsj+PQclytO1THD7gVuASooRi0pP8LDCRIEyBGBI4YiHIIho+cQLhykxB2hTZwkJEyd4xIl8uak4qRgxJ7Rt0mzw4KNaa4zM+MOaJWQXklOGwvkSUgnCevVbFPPTbJmf8tum0y9twv6+0VWRKxCi9i/fF3lf326F4VTrJkeBPWUGkZ3FxQpuTkVvXP7S1eKElLiND6huiQcGGf3nG3jyUzv+myZqb8apWb1PCi0Od70LumC3Z/X2Qsay1XXqbq7K5WNzeKqRzCHeSzSfa5iAzuooU7Z13jAM16sK+vGurXuPqRWX+GZxbdh3b8DAfCrWA==</latexit><latexit sha1_base64="M5B+B1V26f4JSp9qkb28/DRUnRs=">AAADC3icjVHLSsQwFD3W9/gademmOAi6GVoRdCOIgrgcwRkFK5LWOBPsizQVZMZP8E/cuRO3/oAbEf0A/QtvYkfUQTSl7cm555zkJn4aikw5zlOf1T8wODQ8MloaG5+YnCpPzzSyJJcBrwdJmMgDn2U8FDGvK6FCfpBKziI/5Pv+2Zau759zmYkk3lMXKT+KWDMWpyJgiqjj8rbXYqq9dbnYcW1PsrgZcttLlIh4Zne8Wkt02aX1jtsj+PQclytO1THD7gVuASooRi0pP8LDCRIEyBGBI4YiHIIho+cQLhykxB2hTZwkJEyd4xIl8uak4qRgxJ7Rt0mzw4KNaa4zM+MOaJWQXklOGwvkSUgnCevVbFPPTbJmf8tum0y9twv6+0VWRKxCi9i/fF3lf326F4VTrJkeBPWUGkZ3FxQpuTkVvXP7S1eKElLiND6huiQcGGf3nG3jyUzv+myZqb8apWb1PCi0Od70LumC3Z/X2Qsay1XXqbq7K5WNzeKqRzCHeSzSfa5iAzuooU7Z13jAM16sK+vGurXuPqRWX+GZxbdh3b8DAfCrWA==</latexit><latexit sha1_base64="ajI2UaLW8pP3N0Z+Tbtvo6zJbUA=">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</latexit>
Acting on the basis states we obtain:
With the use of linearity of the operator ˆC<latexit sha1_base64="jjWc3ChqFbg97FASrFK6HzXmHTY=">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</latexit><latexit sha1_base64="jjWc3ChqFbg97FASrFK6HzXmHTY=">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</latexit><latexit sha1_base64="jjWc3ChqFbg97FASrFK6HzXmHTY=">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</latexit><latexit sha1_base64="SD4FtEdYrr4dzl3QW5YZMi+u4o0=">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</latexit>
we find
ˆC(| i ⌦ | i) = ↵|0i ⌦ |0i + |1i ⌦ |1i<latexit sha1_base64="M5gMVuXuLjnJKHjYIyoyFxH6J98=">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</latexit><latexit sha1_base64="M5gMVuXuLjnJKHjYIyoyFxH6J98=">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</latexit><latexit sha1_base64="M5gMVuXuLjnJKHjYIyoyFxH6J98=">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</latexit><latexit sha1_base64="eRCboPPMzoPslZipbOUI1GR/kSo=">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</latexit>
while the expected product state should be
| i ⌦ | i = ↵2
|0i ⌦ |0i + ↵ (|0i ⌦ |1i + |1i ⌦ |0i) + 2
|1i ⌦ |1i<latexit sha1_base64="cTZfPJHc3vKlBvRkjjG+2w+q2Ng=">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</latexit><latexit sha1_base64="cTZfPJHc3vKlBvRkjjG+2w+q2Ng=">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</latexit><latexit sha1_base64="cTZfPJHc3vKlBvRkjjG+2w+q2Ng=">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</latexit><latexit sha1_base64="j/1zZbkvjWzcJawbRaWDYU0uLuo=">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</latexit>
The proof can easily be extended to any state | i<latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="/TMCn7Xyy44eDQTP/RuL94TJ5DE=">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</latexit>
BB84 QKD protocol
B1 = {|0i, |1i}<latexit sha1_base64="3T/6D30Fp2j7qoCySq5qgK1Dejg=">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</latexit><latexit sha1_base64="3T/6D30Fp2j7qoCySq5qgK1Dejg=">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</latexit><latexit sha1_base64="3T/6D30Fp2j7qoCySq5qgK1Dejg=">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</latexit><latexit sha1_base64="6CGaZj0NBNNHJn++ArEpA9C7jpg=">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</latexit>
Let us consider two mutually unbiased bases:
B2 = {|+i, | i}<latexit sha1_base64="kkYJKc78j+S4MO58nmsNnOKtE6g=">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</latexit><latexit sha1_base64="kkYJKc78j+S4MO58nmsNnOKtE6g=">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</latexit><latexit sha1_base64="kkYJKc78j+S4MO58nmsNnOKtE6g=">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</latexit><latexit sha1_base64="fSOglpW4eeTXdyXiH3YGRxu6Xso=">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</latexit>
and
so that |h | i|2
=
1
2<latexit sha1_base64="5aZ5R3OMQrGuXC6UjyVhDyohZtE=">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</latexit><latexit sha1_base64="5aZ5R3OMQrGuXC6UjyVhDyohZtE=">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</latexit><latexit sha1_base64="5aZ5R3OMQrGuXC6UjyVhDyohZtE=">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</latexit><latexit sha1_base64="/XVgK3pu4kRwHKeC1zQyCe3yLp0=">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</latexit>
8 | i 2 B1<latexit sha1_base64="Qjr2l18Zu/I7gQb1gkVhJJigCtA=">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</latexit><latexit sha1_base64="Qjr2l18Zu/I7gQb1gkVhJJigCtA=">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</latexit><latexit sha1_base64="Qjr2l18Zu/I7gQb1gkVhJJigCtA=">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</latexit><latexit sha1_base64="KTvPuZkoYDkSakg/Yz7TuF2tDTk=">AAAC8XicjVHLThsxFD1MaZvSB6FddmMRVeqiimbYwBKlG5ap1AQkJoo8xkksPA95PJWiND/RXXeILT/AtvwE6h+0f9FrYyTaqAKPZub43HuOfe/NKq1qG8c/16JH64+fPG0923j+4uWrzfbW62FdNkbIgSh1aY4yXkutCjmwymp5VBnJ80zLw+z0o4sffpGmVmXx2c4rOcr5tFATJbglatz+kE5Kw7VmKWNfWVrNFEsNL6ZaslQVjKU5tzPB9aK3HCfjdifuxn6xVZAE0EFY/bJ9jRQnKCHQIIdEAUtYg6Om5xgJYlTEjbAgzhBSPi6xxAZpG8qSlMGJPaXvlHbHgS1o7zxrrxZ0iqbXkJLhHWlKyjOE3WnMxxvv7Nj/eS+8p7vbnP5Z8MqJtZgRe5/uNvOhOleLxQR7vgZFNVWecdWJ4NL4rribsztVWXKoiHP4hOKGsPDK2z4zr6l97a633Md/+UzHur0IuQ1+u1vSgJN/x7kKhjvdJO4mn3Y6+70w6hbeYhvvaZ672McB+hiQ9zdc4geuojr6Hp1F5zep0VrQvMFfK7r4A/3yoDs=</latexit>
8 | i 2 B2<latexit sha1_base64="9y+aNRlyL8nYYBLI8+yvVtqm4UE=">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</latexit><latexit sha1_base64="9y+aNRlyL8nYYBLI8+yvVtqm4UE=">AAAC8XicjVHLbhMxFD2d0pIWWkJZdmMRIbFA0UyFBMuqbLosEmkrdaLI4ziJFc9DtgcpSvMT3bFD3fYHum1/AvEH8Bdcm4kERAg8mpnjc+859r03q7SyLo6/rkXrDzY2H7a2th893tl90n66d2rL2gjZE6UuzXnGrdSqkD2nnJbnlZE8z7Q8y6bvfPzsozRWlcUHN6tkP+fjQo2U4I6oQftVOioN15qljF2ytLKKpYYXYy1ZqgrG0py7ieB6frQYHAzanbgbh8VWQdKADpp1Ura/IMUQJQRq5JAo4AhrcFh6LpAgRkVcH3PiDCEV4hILbJO2pixJGZzYKX3HtLto2IL23tMGtaBTNL2GlAwvSFNSniHsT2MhXgdnz/7Nex48/d1m9M8ar5xYhwmx/9ItM/9X52txGOFtqEFRTVVgfHWicalDV/zN2S9VOXKoiPN4SHFDWATlss8saGyo3feWh/i3kOlZvxdNbo3v/pY04OTPca6C04NuEneT9687h0fNqFvYx3O8pHm+wSGOcYIeeV/hFne4j2z0KfocXf9MjdYazTP8tqKbHxxVoEk=</latexit><latexit sha1_base64="9y+aNRlyL8nYYBLI8+yvVtqm4UE=">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</latexit><latexit sha1_base64="1eseesH2ECVoJGAmoUxdu5dMQfQ=">AAAC8XicjVHLbhMxFD0ZoIQUSqBLNhZRpS6qaCabsozKhmUqNWmlThV5HCex6nnI9iBVIT/Bjh1iyw+wLT+B+gflL7g2U4m2QuDRzByfe8+x771ZpZV1cXzVih48fLTxuP2ks/n02dbz7ouXE1vWRsixKHVpTjJupVaFHDvltDypjOR5puVxdv7Wx4/fS2NVWRy5i0qe5XxRqLkS3BE17e6l89JwrVnK2AeWVlax1PBioSVLVcFYmnO3FFyvDtbTwbTbi/txWOw+SBrQQ7NGZfcHUsxQQqBGDokCjrAGh6XnFAliVMSdYUWcIaRCXGKNDmlrypKUwYk9p++CdqcNW9Dee9qgFnSKpteQkmGHNCXlGcL+NBbidXD27N+8V8HT3+2C/lnjlRPrsCT2X7qbzP/V+Voc5ngTalBUUxUYX51oXOrQFX9z9kdVjhwq4jyeUdwQFkF502cWNDbU7nvLQ/w6ZHrW70WTW+OnvyUNOLk7zvtgMugncT85HPSGB82o23iF19ilee5jiHcYYUzeH/ENl/ge2ehT9Dn68js1ajWabdxa0ddfG7WgRw==</latexit>
and
Digital bits of the secret key are encoded as follows:
|0i ! 0<latexit sha1_base64="S7XMD7HLj+CGFS71BDKHkmwoQwc=">AAAC33icjVHLSsQwFD3W97vqTjfFQXA1tCLoUnTjcgTnAc4wpJ1MJ0ynLWmqiAru3Ilbf8Ct/o34B/oX3sQK6iCa0uTk3HtOcnP9NBKZct2XEWt0bHxicmp6ZnZufmHRXlquZUkuA14NkiiRDZ9lPBIxryqhIt5IJWcDP+J1v3+g4/VTLjORxMfqPOWtAQtj0RUBU0S17dVLx3WaksVhxGkVYU8xKZMzYtt2yS27ZjjDwCtACcWoJPYzmuggQYAcA3DEUIQjMGT0ncCDi5S4Fi6Ik4SEiXNcYYa0OWVxymDE9mkOaXdSsDHttWdm1AGdEtEvSelggzQJ5UnC+jTHxHPjrNnfvC+Mp77bOa1+4TUgVqFH7F+6z8z/6nQtCl3smhoE1ZQaRlcXFC65eRV9c+dLVYocUuI07lBcEg6M8vOdHaPJTO36bZmJv5pMzep9UOTmeNO3pAZ7P9s5DGpbZc8te0fbpb39otVTWMM6NqmfO9jDISqokvc1HvCIJ4tZN9atdfeRao0UmhV8G9b9O01dmSY=</latexit><latexit sha1_base64="S7XMD7HLj+CGFS71BDKHkmwoQwc=">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</latexit><latexit sha1_base64="S7XMD7HLj+CGFS71BDKHkmwoQwc=">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</latexit><latexit sha1_base64="syHL1or9hNyRDyBpTZ5K0cJohMs=">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</latexit>
|1i ! 1<latexit sha1_base64="V/QTWHTGSK8ZKeTEhDA7v7Audqk=">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</latexit><latexit sha1_base64="V/QTWHTGSK8ZKeTEhDA7v7Audqk=">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</latexit><latexit sha1_base64="V/QTWHTGSK8ZKeTEhDA7v7Audqk=">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</latexit><latexit sha1_base64="lrzAT2MY1fTdiobk9m9sdER3h3o=">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</latexit>
|+i ! 0<latexit sha1_base64="6Lpx7pNX8rcAo0X96ILWdBkETI4=">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</latexit><latexit sha1_base64="6Lpx7pNX8rcAo0X96ILWdBkETI4=">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</latexit><latexit sha1_base64="6Lpx7pNX8rcAo0X96ILWdBkETI4=">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</latexit><latexit sha1_base64="qU6b6fd0t91aAq/vb89e5I/DWhw=">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</latexit>
| i ! 1<latexit sha1_base64="W18LaV8edDsAy9q6C+O+xbssvM4=">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</latexit><latexit sha1_base64="W18LaV8edDsAy9q6C+O+xbssvM4=">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</latexit><latexit sha1_base64="W18LaV8edDsAy9q6C+O+xbssvM4=">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</latexit><latexit sha1_base64="kmgOcCfjDFin7Tt0N71ugSul2pg=">AAAC3nicjVG7TsMwFD0Nr/IOMCGWiAqJhSrpAmMFCyNIFJAoKk7qtlbTJHIcUFUQGxti5QdY4XMQfwB/wbVJJR5C4Cj28bn3HPv6+kkoUuW6LwVrZHRsfKI4OTU9Mzs3by8sHqZxJgNeC+Iwlsc+S3koIl5TQoX8OJGc9fyQH/ndHR0/OucyFXF0oPoJP+2xdiRaImCKqIa9fOlsOHXJonbIaRXtjmJSxheO17BLbtk1w/kJvByUkI+92H5GHU3ECJChB44IinAIhpS+E3hwkRB3igFxkpAwcY4rTJE2oyxOGYzYLs1t2p3kbER77ZkadUCnhPRLUjpYI01MeZKwPs0x8cw4a/Y374Hx1Hfr0+rnXj1iFTrE/qUbZv5Xp2tRaGHL1CCopsQwurogd8nMq+ibO5+qUuSQEKdxk+KScGCUw3d2jCY1teu3ZSb+ajI1q/dBnpvhTd+SGux9b+dPcFgpe27Z26+Uqtt5q4tYwSrWqZ+bqGIXe6iR9zUe8Ign68y6sW6tu49Uq5BrlvBlWPfvzMeY+A==</latexit>
Sender (Alice) is randomly choosing between the 4
polarization states to generate the secret key.
Reciever (Bob) analyses the photon states in one of the two
bases, withouth the prior knowledge of the polarization
bases used by Alice. Using a classical channel, Bob announces
his measurement bases. Basis reconciliation is made at this
point. The last step is to verify if no attack has been made.
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DOI: 10.1007/978-3-319-30201-0_27
A simple uncorrelated attack
An eavesdropper (Eve) does not know what the bases
chosen by Alice are. How probable is that Eve is not
detected?
Alice (A)
Eve’s analysers
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1<latexit sha1_base64="nY8hzPj3CKCZuv3SM159RUZ0WgQ=">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</latexit><latexit sha1_base64="nY8hzPj3CKCZuv3SM159RUZ0WgQ=">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</latexit><latexit sha1_base64="nY8hzPj3CKCZuv3SM159RUZ0WgQ=">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</latexit><latexit sha1_base64="XPupLPfcVGDyo5uXnY6ujO9GvVU=">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</latexit>
Bob (B)
The probability is: P(0) =
1
2
· 1 +
1
2
·
1
2
=
3
4<latexit sha1_base64="2UEwVMutiXvb+VxrvhnJcc4YjWk=">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</latexit><latexit sha1_base64="2UEwVMutiXvb+VxrvhnJcc4YjWk=">AAADD3icjVHLSsNAFD3GV31XXboZLIIilEQF3QhFN+KqglXBiiTTqQbTJEwmQgn9CP/EnTtx6w8ornSpf+GdMRW1iE5Icu6595yZO9eLAz9Rtv3UZ/UPDA4NF0ZGx8YnJqeK0zMHSZRKLmo8CiJ55LmJCPxQ1JSvAnEUS+G2vEAcehfbOn94KWTiR+G+asfipOWehX7T564i6rS4W120l9gmqzelyzOnk610WJ03IuWw5V7yG/OpWu1kaxSeFkt22TaL9QInByXkqxoVH1FHAxE4UrQgEEIRDuAioecYDmzExJ0gI04S8k1eoINR0qZUJajCJfaCvmcUHedsSLH2TIya0y4BvZKUDAukiahOEta7MZNPjbNmf/POjKc+W5v+Xu7VIlbhnNi/dN3K/+p0LwpNbJgefOopNozujucuqbkVfXL2pStFDjFxGjcoLwlzo+zeMzOaxPSu79Y1+VdTqVkd87w2xZs+JQ3Y+TnOXnCwUnbssrO3Vqps5aMuYA7zWKR5rqOCHVRRI+9rPOAZL9aVdWPdWncfpVZfrpnFt2XdvwMVaqpz</latexit><latexit sha1_base64="2UEwVMutiXvb+VxrvhnJcc4YjWk=">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</latexit><latexit sha1_base64="eRrrjHtLf4XZI6WEMzIm3x1R3HY=">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</latexit>
✓
3
4
◆N
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For N bits:
QBER - Quantum Bit Error Rate
QBER (e) - error rate per qubit
qubits with error
number of qubits
e :=
Ne
N<latexit sha1_base64="vylH4oT7wuFf9eDE4LMrMATRaxc=">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</latexit><latexit sha1_base64="vylH4oT7wuFf9eDE4LMrMATRaxc=">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</latexit><latexit sha1_base64="vylH4oT7wuFf9eDE4LMrMATRaxc=">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</latexit><latexit sha1_base64="WNnJp9g33+9rN4RtmGWNFMPShnA=">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</latexit>
In the case of uncorrelated attack on BB84 e =
f
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f<latexit sha1_base64="7QQfQx4iNX04F8go9Nvv8s3hbAI=">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</latexit><latexit sha1_base64="7QQfQx4iNX04F8go9Nvv8s3hbAI=">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</latexit><latexit sha1_base64="7QQfQx4iNX04F8go9Nvv8s3hbAI=">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</latexit><latexit sha1_base64="gW0ua91YbXX5ZKtY6q81l7g764Y=">AAACxHicjVHLSsNAFD2Nr1pfVZdugkVwVZJudFkUxGUL9gG1SDKd1tBpEjIToRT9Abf6beIf6F94Z5yCWkQnJDlz7j1n5t4bpiKSyvNeC87S8srqWnG9tLG5tb1T3t1ryyTPGG+xRCRZNwwkF1HMWypSgnfTjAeTUPBOOD7X8c4dz2SUxFdqmvL+JBjF0TBigSKqObwpV7yqZ5a7CHwLKrCrkZRfcI0BEjDkmIAjhiIsEEDS04MPDylxfcyIywhFJs5xjxJpc8rilBEQO6bviHY9y8a0157SqBmdIujNSOniiDQJ5WWE9WmuiefGWbO/ec+Mp77blP6h9ZoQq3BL7F+6eeZ/dboWhSFOTQ0R1ZQaRlfHrEtuuqJv7n6pSpFDSpzGA4pnhJlRzvvsGo00teveBib+ZjI1q/fM5uZ417ekAfs/x7kI2rWq71X9Zq1SP7OjLuIAhzimeZ6gjks00DLej3jCs3PhCEc6+WeqU7CafXxbzsMHP7yPaQ==</latexit>
- fraction of qubits analyzed by Eve (E)
Shannon entropy per bit h(e) = e log(e) (1 e) log(1 e)<latexit sha1_base64="uj+6jDBVdaoVyWMQudtXgVfcLGQ=">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</latexit><latexit sha1_base64="uj+6jDBVdaoVyWMQudtXgVfcLGQ=">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</latexit><latexit sha1_base64="uj+6jDBVdaoVyWMQudtXgVfcLGQ=">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</latexit><latexit sha1_base64="zPuvMWRyiJ1652Plml4Qtz6wRE4=">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</latexit>
I(A : B) = 1 h(e)<latexit sha1_base64="PB1XmOXxRLEkKzTi6Qx6CbQu7ok=">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</latexit><latexit sha1_base64="PB1XmOXxRLEkKzTi6Qx6CbQu7ok=">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</latexit><latexit sha1_base64="PB1XmOXxRLEkKzTi6Qx6CbQu7ok=">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</latexit><latexit sha1_base64="94dCv2yFWLg9WuIEDCzLkfCfIfE=">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</latexit>
Mutual information between A and B:
Mutual information between A and E: I(A : E) = f/2 = 2e<latexit sha1_base64="pWLLOiuZZklOFWFiDTu6dFmG/es=">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</latexit><latexit sha1_base64="pWLLOiuZZklOFWFiDTu6dFmG/es=">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</latexit><latexit sha1_base64="pWLLOiuZZklOFWFiDTu6dFmG/es=">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</latexit><latexit sha1_base64="IEXRH8VSgmSZnliyppQniZxZ72M=">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</latexit>
If I(A : E) I(A : B)<latexit sha1_base64="G+lfmHLoFrDm1HBRuMree2cROrg=">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</latexit><latexit sha1_base64="G+lfmHLoFrDm1HBRuMree2cROrg=">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</latexit><latexit sha1_base64="G+lfmHLoFrDm1HBRuMree2cROrg=">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</latexit><latexit sha1_base64="BKF7BURvBNjRRUDyLQAXlyTNFPk=">AAAC13icjVHLSsNAFD2Nr1pftS7dBIvQbkriRnFVK4LuKtiHtKUk6bSG5mUyEUsRd+LWH3CrfyT+gf6Fd8YU1CI6IcmZc+85M/deM3DsiGvaa0qZmZ2bX0gvZpaWV1bXsuu5euTHocVqlu/4YdM0IubYHqtxmzusGYTMcE2HNczhoYg3rlgY2b53xkcB67jGwLP7tmVworrZ3EnhYP+oqLYH7FIVuFLsZvNaSZNLnQZ6AvJIVtXPvqCNHnxYiOGCwQMn7MBARE8LOjQExHUwJi4kZMs4ww0ypI0pi1GGQeyQvgPatRLWo73wjKTaolMcekNSqtgmjU95IWFxmirjsXQW7G/eY+kp7jaiv5l4ucRyXBD7l26S+V+dqIWjjz1Zg001BZIR1VmJSyy7Im6ufqmKk0NAnMA9ioeELamc9FmVmkjWLnpryPibzBSs2FtJbox3cUsasP5znNOgvlPStZJ+upMvV5JRp7GJLRRonrso4xhV1Mj7Go94wrNyrtwqd8r9Z6qSSjQb+LaUhw9SYpRo</latexit>
then E has more information than B,
which is when e & 17 %<latexit sha1_base64="BnLo/j4jA7Zz4b9ocFMo6q7lAxY=">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</latexit><latexit sha1_base64="BnLo/j4jA7Zz4b9ocFMo6q7lAxY=">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</latexit><latexit sha1_base64="BnLo/j4jA7Zz4b9ocFMo6q7lAxY=">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</latexit><latexit sha1_base64="HGZ6HTCy1YzGiTL5Kp6r1IMtd1M=">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</latexit>
Limitations on distance due to losses in optical fiber…
QKD is already in commercial use
The signal may be amplified with the use quantum repeaters
www.cqc2t.org
Exponential suppression
of photons with distance
in the fiber.
Possible solution:
Inverse-square suppression of photons in vacuum…
Recently even 10 Mb/s in fiber (arXiv: 1807.04484)
~ 1 Mb/s over 50 km of standard optical fibre
~ 1 bit per hour over 400 kilometres of ultralow-loss fibre
Intercontinental QKD - Chinese Micius satellite (2017).
It is much easier to transmit quantum signal in air/vacuum.
arXiv:1801.04418
~ 3 kb/s at ~1000 km ~ 9 kb/s at ~600 km
XINHUA / JIN LIWANG / MCG
Quantum encrypted one-time-pad file transfer.
Video transfer encrypted with the use Advanced Encryption
Standard (AES) -192. A new 192 bit quantum distributed
key has been provided every second.
arXiv:1801.04418
Space based QKD configurations
R. Bendington et al. EPJ Quantum Technology (2016) 3:12
Quantum Space Technologies
CubeSats
Canadian Space Agency
Quantum Space Technologies
Ekert (E91) protocol
| ABi =
1
p
2
(|0iA|0iB + |1iA|1iB)
=
1
p
2
(|✓iA|✓iB + |✓?iA|✓?iB)
<latexit sha1_base64="dEM4ehyGybv1R87Cla/wgkzSeQw=">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</latexit><latexit sha1_base64="dEM4ehyGybv1R87Cla/wgkzSeQw=">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</latexit><latexit sha1_base64="dEM4ehyGybv1R87Cla/wgkzSeQw=">AAADrXicjVHbbtQwEJ00XEq4bekjLxYrqiKkJamQ2pdK7fLCE1oktq1Ul8hxvVmr2STYTqUqG36z4g/KXzB2E7E0QuAoycyZc449nqTMpDZh+MNb8+/df/Bw/VHw+MnTZ88HGy+OdFEpLqa8yAp1kjAtMpmLqZEmEyelEmyRZOI4ufhg68eXQmlZ5F/MVSnOFizN5UxyZhCKBzdLOtEyrg/HDaGK5WkmyNY+oTPFeB01NdXflKl3miagmZiZbbIMO158uJqM3y6j1crvZEyVTOfmDaE02NrvO3fG1MyFYasedxDc4haJa1oKVTZ9bq/SbR7Eg2E4Ct0i/SBqgyG0a1IMroHCORTAoYIFCMjBYJwBA43PKUQQQonYGdSIKYykqwtoIEBthSyBDIboBX5TzE5bNMfcemqn5rhLhq9CJYHXqCmQpzC2uxFXr5yzRf/mXTtPe7Yr/Cet1wJRA3NE/6XrmP+rs70YmMGe60FiT6VDbHe8dancrdiTk5WuDDqUiNn4HOsKY+6U3T0Tp9Gud3u3zNVvHNOiNuctt4Kf9pQ44OjuOPvB0c4oCkfR5/fDg3E76nV4Ca9gG+e5CwfwESYwBe598ozXeN/9d/7Up/7XW+qa12o24Y/lp78AOCrjig==</latexit><latexit sha1_base64="pbvgud4TGvxrHohqiWrqbphdqcg=">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</latexit>
EPR pairs are created between Alice (A) and Bob (B):
Security is confirmed by virtue of the Bell’s inequality.
arXiv:1406.1685
SPEQS (Small Photon-Entangling Quantum System)
arXiv:1603.06659
Galassia CubeSat
arXiv:1603.06659
SpooQySat
R. Bendington et al. EPJ Quantum Technology (2016) 3:12
Nanobob - CubeSat 12U (quantum uplink only)
Q3Sat - CubeSat 3U (quantum uplink only)
arXiv:1711.01886
EPJ Quantum Technology (2018) 5:4
Activated Entangled Photon Source
www.fraunhofer.de
Passive photon exchange with GNSS
arXiv:1804.05022
Exchange of single photons by exploiting retroreflector array
mounted on GLONASS satellites.
The first exchange of a few photons per
pulse along a channel length of 20000 km,
reaching a SNR about 0.5 and a detection
rate around 60 Hz.
Effects of General Relativity
QFT in Schwarzschild metric
QFT in Kerr metric
Curvedspacetime
arXiv:1309.3088
QBER ⇠
2
⌦2
B,0
8 2
⇠ 0.7%
<latexit sha1_base64="6+7E6vPkc1zZ8LNLmjObJeztU14=">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</latexit><latexit sha1_base64="6+7E6vPkc1zZ8LNLmjObJeztU14=">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</latexit><latexit sha1_base64="6+7E6vPkc1zZ8LNLmjObJeztU14=">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</latexit><latexit sha1_base64="FavJWh22ihiJDPkSmc/3i51gvOA=">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</latexit>
arXiv:1409.0234
arXiv:1511.04256
QBER ⇠ 10 2
(GEO)<latexit sha1_base64="yCU3TAZX3mEvzSIYKQmZPcGebgY=">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</latexit><latexit sha1_base64="yCU3TAZX3mEvzSIYKQmZPcGebgY=">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</latexit><latexit sha1_base64="yCU3TAZX3mEvzSIYKQmZPcGebgY=">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</latexit><latexit sha1_base64="Vn8F6Tn4iWMtn7VJmyVGNqS6bL8=">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</latexit>
QBER ⇠ 10 4
(LEO)<latexit sha1_base64="RmCojH7SQhr8ZjI9r4SfPWaQcF0=">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</latexit><latexit sha1_base64="RmCojH7SQhr8ZjI9r4SfPWaQcF0=">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</latexit><latexit sha1_base64="RmCojH7SQhr8ZjI9r4SfPWaQcF0=">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</latexit><latexit sha1_base64="8wfK7Xt4bpUm0WgMDIPRtJEes3w=">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</latexit>
QBER ⇠ 10 8
for rB ⇠
3
2
rA
<latexit sha1_base64="kDf55PUUXrYP6HYdc+gj/O49TKs=">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</latexit><latexit sha1_base64="kDf55PUUXrYP6HYdc+gj/O49TKs=">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</latexit><latexit sha1_base64="kDf55PUUXrYP6HYdc+gj/O49TKs=">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</latexit><latexit sha1_base64="ijWXi4fnEcv0PoExlDLrfJdBLTs=">AAADCHicjVHLLgRBFD3a+z1Y2nRMJDYm3WNhloxILBGDxDDpLjVU9CvV1UI6/QP+xM5ObP2AJf6Av3CrtMQjQlW6+9xzz7ldt66fBCJVjvPcY/X29Q8MDg2PjI6NT0xWpqZ30ziTjLdYHMRy3/dSHoiIt5RQAd9PJPdCP+B7/tmazu+dc5mKONpRlwk/DL2TSHQF8xRRncpaW/ELlW8117cLu52K0Hado3yxQYHeJtmNZaEj2Wm+S9pd6bF8qcjrBZGrnUrVqTlm2T+BW4IqyrUZVx7RxjFiMGQIwRFBEQ7gIaV9ABcOEuIOkRMnCQmT5ygwQt6MVJwUHrFn9D6h6KBkI4p1zdS4Gf0loEeS08Y8eWLSScL6b7bJZ6ayZn+rnZua+myX9PXLWiGxCqfE/uX7UP7Xp3tR6KJhehDUU2IY3R0rq2TmVvTJ7U9dKaqQEKfxMeUlYWacH/dsG09qetd365n8i1FqVses1GZ41aekAbvfx/kT7NZrrlNzt+rVlWY56iHMYg4LNM9lrGADm2hR7Ws84AnP1pV1Y91ad+9Sq6f0zODLsu7fALh2qPM=</latexit>
:=
⌦B
⌦A
1 = S + rot + c
<latexit sha1_base64="0fffzyw9GzMFj46dRoaroEKKSgY=">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</latexit><latexit sha1_base64="0fffzyw9GzMFj46dRoaroEKKSgY=">AAADDHicjVFdSxtBFD1ubbXph2v72JfBUBBKw64IihCw9qF906IxARPC7GQSl+wXs7MFCfkL/hPffBNf/QN9KIX63v6L3hkn0DaUOsvunnvuPWfmzo2KJC51EHxb8B4sPny0tPy49uTps+cr/uqL4zKvlJAtkSe56kS8lEmcyZaOdSI7hZI8jRLZjsbvTb79WaoyzrMjfVbIXspHWTyMBddE9f0P3YFMNGc7TdYdKi4m3f1Ujnh/bzpD76ZvQ1Zr3tX1D984MFG5ns4Cwfp+PWgEdrF5EDpQh1sHuf8VXQyQQ6BCCokMmnACjpKeE4QIUBDXw4Q4RSi2eYkpaqStqEpSBSd2TN8RRSeOzSg2nqVVC9oloVeRkuE1aXKqU4TNbszmK+ts2H95T6ynOdsZ/SPnlRKrcUrs/3SzyvvqTC8aQ2zbHmLqqbCM6U44l8reijk5+60rTQ4FcQYPKK8IC6uc3TOzmtL2bu6W2/wPW2lYEwtXW+GnOSUNOPx7nPPgeKMRBo3w02Z9d8+NehmvsIZ1mucWdvERB2iR9wW+4DtuvXPv0rvyru9KvQWneYk/lnfzC/rgq08=</latexit><latexit sha1_base64="0fffzyw9GzMFj46dRoaroEKKSgY=">AAADDHicjVFdSxtBFD1ubbXph2v72JfBUBBKw64IihCw9qF906IxARPC7GQSl+wXs7MFCfkL/hPffBNf/QN9KIX63v6L3hkn0DaUOsvunnvuPWfmzo2KJC51EHxb8B4sPny0tPy49uTps+cr/uqL4zKvlJAtkSe56kS8lEmcyZaOdSI7hZI8jRLZjsbvTb79WaoyzrMjfVbIXspHWTyMBddE9f0P3YFMNGc7TdYdKi4m3f1Ujnh/bzpD76ZvQ1Zr3tX1D984MFG5ns4Cwfp+PWgEdrF5EDpQh1sHuf8VXQyQQ6BCCokMmnACjpKeE4QIUBDXw4Q4RSi2eYkpaqStqEpSBSd2TN8RRSeOzSg2nqVVC9oloVeRkuE1aXKqU4TNbszmK+ts2H95T6ynOdsZ/SPnlRKrcUrs/3SzyvvqTC8aQ2zbHmLqqbCM6U44l8reijk5+60rTQ4FcQYPKK8IC6uc3TOzmtL2bu6W2/wPW2lYEwtXW+GnOSUNOPx7nPPgeKMRBo3w02Z9d8+NehmvsIZ1mucWdvERB2iR9wW+4DtuvXPv0rvyru9KvQWneYk/lnfzC/rgq08=</latexit><latexit sha1_base64="YLZg2h5r9Lu9XVM49VNbsVMbQO8=">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</latexit>
arXiv:1811.07322
ESA ScyLight - SeCure and Laser
Communication Technology.
Satelitary quantum network -
,,quantum internet’’
One of the philars of the EU Quantum Flagship program.
QuTech/TU Delft/Scixel
Security of financial transactions, trading and
cryptocurrencies.
Secured (Earth to Earth) communication for civil
and military purposes.
Secured channel for telemedicne and medical
data exchange.
Secured comunication with satellites (military and
civil).
Solution to the emerging problem of insecurity of
classical cryptographic systems.
Quantum teleportation to LEO
We already know how to send (teleportate) quantum
information into space. This is crucial for the purpose
of quantum communication.
Twophotons
Photon sent to space
Entanglement
Entanglement
Photon remaining on Earth
Teleported sate on Earth
Teleported sate on LEO
Classical channel
A
B | ABi =
1
p
2
(|0iA|0iB + |1iA|1iB)
<latexit sha1_base64="rzJMolEr0/SGVXuApHzaNumikio=">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</latexit><latexit sha1_base64="rzJMolEr0/SGVXuApHzaNumikio=">AAADNXicjVFNSyQxEK1p1891d0c9egk7LCjC0C0LehF0vHgcwVHBliEdM2Mw090maUF6+nf5TxQPe1tET/4BD1aykd1ZEU3T3VWv3ntJpZJcCm3C8LYWjH0an5icmp75PPvl67f63Py+zgrFeIdlMlOHCdVcipR3jDCSH+aK00Ei+UFytm3rBxdcaZGle+Yy58cD2k9FTzBqEOrW82Hc1qJbbrWqWNG0LznZIHFPUVZGVRnrc2XK1aqKJe+ZJTIkIfG07tZI1loZkmik9jdrEVyxEv1Ts0y69UbYDN0ir4PIBw3wq53VbyCGE8iAQQED4JCCwVgCBY3PEUQQQo7YMZSIKYyEq3OoYAa1BbI4MiiiZ/jtY3bk0RRz66mdmuEuEl+FSgI/UJMhT2FsdyOuXjhni77lXTpPe7ZL/Cfea4CogVNE39O9MD+qs70Y6MG660FgT7lDbHfMuxTuVuzJyT9dGXTIEbPxCdYVxswpX+6ZOI12vdu7pa5+75gWtTnz3AIe7ClxwNH/43wd7K82o7AZ7f5sbLb8qKdgEb7DEs5zDTZhB9rQQe9reKqN1yaCq+BX8Du4+0MNal6zACMreHwGXY+3rA==</latexit><latexit sha1_base64="rzJMolEr0/SGVXuApHzaNumikio=">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</latexit><latexit sha1_base64="iNNQTA8A2gvYo+n8u1nOq6XgSCM=">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</latexit>
B
A
| i = ↵|0i + |1i<latexit sha1_base64="KnjSa2qv+IpETeXL6+1Kh1Ctio4=">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</latexit><latexit sha1_base64="KnjSa2qv+IpETeXL6+1Kh1Ctio4=">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</latexit><latexit sha1_base64="KnjSa2qv+IpETeXL6+1Kh1Ctio4=">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</latexit><latexit sha1_base64="PURkbTB2QPwPjzeIWLcco5jcik8=">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</latexit>
In order to teleportate the state
EPR pair | ABi =
1
p
2
(|0iA|0iB + |1iA|1iB)
<latexit sha1_base64="rzJMolEr0/SGVXuApHzaNumikio=">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</latexit><latexit sha1_base64="rzJMolEr0/SGVXuApHzaNumikio=">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</latexit><latexit sha1_base64="rzJMolEr0/SGVXuApHzaNumikio=">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</latexit><latexit sha1_base64="iNNQTA8A2gvYo+n8u1nOq6XgSCM=">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</latexit>
is created
By acting with CNOT and H gates on we obtain| i| ABi<latexit sha1_base64="qEIiw0KZ3vV8phiixZHYhwEW+DU=">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</latexit><latexit sha1_base64="qEIiw0KZ3vV8phiixZHYhwEW+DU=">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</latexit><latexit sha1_base64="qEIiw0KZ3vV8phiixZHYhwEW+DU=">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</latexit><latexit sha1_base64="pzBACqwwHB1HTYw/c117EiycHdU=">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</latexit>
1
2
|0i|0iA(↵|0iB + |0iB) +
1
2
|0i|1iA(↵|1iB + |0iB)
<latexit sha1_base64="WdAfL4PsWwsbR6h5ifcmZ/8Pfmk=">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</latexit><latexit sha1_base64="WdAfL4PsWwsbR6h5ifcmZ/8Pfmk=">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</latexit><latexit sha1_base64="WdAfL4PsWwsbR6h5ifcmZ/8Pfmk=">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</latexit><latexit sha1_base64="SM2ov6WRDWgHSEQlFywkdxdkrpY=">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</latexit>
+
1
2
|1i|0iA(↵|0iB |0iB) +
1
2
|1i|1iA(↵|1iB |0iB)
<latexit sha1_base64="YnlGP8UKLo2hV0nb+IfWdRgjH+M=">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</latexit><latexit sha1_base64="YnlGP8UKLo2hV0nb+IfWdRgjH+M=">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</latexit><latexit sha1_base64="YnlGP8UKLo2hV0nb+IfWdRgjH+M=">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</latexit><latexit sha1_base64="Xpakrh/KemvdnTYJHAWhphN1Vgc=">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</latexit>
If we measured |0i|0iA<latexit sha1_base64="XaWVP4uAUQH0rglAjrwXhJLn+rs=">AAAC33icjVHLSsNAFD2Nr1pfUXe6GSyCq5KIoMuqG5cVrBZaKZM41mBeTCZCqYI7d+LWH3CrfyP+gf6Fd8YUfCA6IcmZc+85M/deLw2DTDnOS8kaGR0bnyhPVqamZ2bn7PmFwyzJpS+afhImsuXxTIRBLJoqUKFopVLwyAvFkXe+q+NHF0JmQRIfqH4qjiPei4PTwOeKqK69dMkc1pE87oWCfcLdbda1q07NMYv9BG4BqihWI7Gf0cEJEvjIEUEghiIcgiOjpw0XDlLijjEgThIKTFzgChXS5pQlKIMTe07fHu3aBRvTXntmRu3TKSG9kpQMq6RJKE8S1qcxE8+Ns2Z/8x4YT323Pv29wisiVuGM2L90w8z/6nQtCqfYMjUEVFNqGF2dX7jkpiv65uxTVYocUuI0PqG4JOwb5bDPzGgyU7vuLTfxV5OpWb33i9wcb/qWNGD3+zh/gsP1muvU3P2Nan2nGHUZy1jBGs1zE3XsoYEmeV/jAY94srh1Y91adx+pVqnQLOLLsu7fAeXQmJI=</latexit><latexit sha1_base64="XaWVP4uAUQH0rglAjrwXhJLn+rs=">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</latexit><latexit sha1_base64="XaWVP4uAUQH0rglAjrwXhJLn+rs=">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</latexit><latexit sha1_base64="U0EjV+Hx0CsatVUtVXPvXDFK+/E=">AAAC33icjVHLSsNAFD2N7/qqutPNYBFclcSNLn1sXCpYW6hSJuNYg2kSJhNBVHDnTtz6A271b8Q/0L/wzjiFahGdkOTMufecmXtvmMVRrn3/reQNDY+Mjo1PlCenpmdmK3Pzh3laKCHrIo1T1Qx5LuMokXUd6Vg2MyV5N4xlIzzfMfHGhVR5lCYH+jKTx13eSaLTSHBNVLuyeM18dqR40okl68PtLdauVP2abxcbBIEDVbi1l1ZecYQTpBAo0IVEAk04BkdOTwsBfGTEHeOKOEUosnGJG5RJW1CWpAxO7Dl9O7RrOTahvfHMrVrQKTG9ipQMK6RJKU8RNqcxGy+ss2F/876ynuZul/QPnVeXWI0zYv/S9TL/qzO1aJxiw9YQUU2ZZUx1wrkUtivm5qyvKk0OGXEGn1BcERZW2eszs5rc1m56y2383WYa1uyFyy3wYW5JAw5+jnMQHK7VAr8W7K9VN7fdqMexhGWs0jzXsYld7KFO3rd4wjNePO7deffew1eqV3KaBXxb3uMn5TCYkA==</latexit>
then the state of the B qubit is
↵|0iB + |1iB<latexit sha1_base64="ZSUXpchY6Cn5Ax8S8A3YtgEJM0w=">AAAC73icjVHLSsNAFD3GV31HXboZLIIolEQEXZa6cVnBasFKmcSxBqdJnEwEqf6DO3fi1h9wq38h/oH+hXfGiC9EJyQ5c+49Z+beG6QyyrTnPfU5/QODQ8OlkdGx8YnJKXd6ZidLchWKRpjIRDUDngkZxaKhIy1FM1WCdwMpdoPjDRPfPRUqi5J4W5+lYr/LO3F0GIVcE9V2l1pcpkecnTOPtRSPO1K0a8utQGjD+R8cY2237FU8u9hP4BegjGLVE/cRLRwgQYgcXQjE0IQlODJ69uDDQ0rcPnrEKUKRjQtcYJS0OWUJyuDEHtO3Q7u9go1pbzwzqw7pFEmvIiXDAmkSylOEzWnMxnPrbNjfvHvW09ztjP5B4dUlVuOI2L9075n/1ZlaNA6xbmuIqKbUMqa6sHDJbVfMzdmnqjQ5pMQZfEBxRTi0yvc+M6vJbO2mt9zGn22mYc0+LHJzvJhb0oD97+P8CXZWKr5X8bdWy9VaMeoS5jCPRZrnGqrYRB0N8r7EHe7x4Jw4V861c/OW6vQVmll8Wc7tK9tMnpo=</latexit><latexit sha1_base64="ZSUXpchY6Cn5Ax8S8A3YtgEJM0w=">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</latexit><latexit sha1_base64="ZSUXpchY6Cn5Ax8S8A3YtgEJM0w=">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</latexit><latexit sha1_base64="V5XfHfgNWdg4j8G95kR88i7Fg+I=">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</latexit>
which is the teleportated version of | i<latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="/TMCn7Xyy44eDQTP/RuL94TJ5DE=">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</latexit>
In the other cases the CNOT and Z operators have to
be appllied to accomplish the teleportation protocol.
Quantum state teleportation to Micius satellite
arXiv:1707.00934
F =
2
3<latexit sha1_base64="vwSPXvWSGOfxTEgx09U3uH9YXVc=">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</latexit><latexit sha1_base64="vwSPXvWSGOfxTEgx09U3uH9YXVc=">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</latexit><latexit sha1_base64="vwSPXvWSGOfxTEgx09U3uH9YXVc=">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</latexit><latexit sha1_base64="MuCDJT20me5UQCwTB1CQc0ua13Y=">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</latexit>
F(⇢1, ⇢2) := tr(ˆ⇢1 ˆ⇢2)<latexit sha1_base64="ej+Zqym94J2bLRdWdgCmXh+Grcw=">AAAC/XicjVHLSsNAFD2Nr1pfUZdugkVoQUpSBEUQioK4rGAfYEtJ4miDaRImE1FK8U/cuRO3/oBb3Yp/oH/hnTGFqohOSObcc+85mTvXiXwvFqb5mtHGxicmp7LTuZnZufkFfXGpHocJd1nNDf2QNx07Zr4XsJrwhM+aEWd2z/FZwznfk/nGBeOxFwZH4ipi7Z59FninnmsLojr61n6hxbthx1pXW7m4vdMS7FL0BR8UjFbXFn2ZGHSs0aBcNDp63iyZahk/gZWCPNJVDfUXtHCCEC4S9MAQQBD2YSOm5xgWTETEtdEnjhPyVJ5hgBxpE6piVGETe07fM4qOUzagWHrGSu3SX3x6OSkNrJEmpDpOWP7NUPlEOUv2N+++8pRnu6LdSb16xAp0if1LN6z8r072InCKLdWDRz1FipHdualLom5FntwY6UqQQ0ScxCeU54RdpRzes6E0sepd3q2t8m+qUrIydtPaBO/ylDRg6/s4f4J6uWSZJetwI1/ZTUedxQpWUaB5bqKCA1RRI+8bPOIJz9q1dqvdafefpVom1Szjy9IePgBmFKU+</latexit><latexit sha1_base64="ej+Zqym94J2bLRdWdgCmXh+Grcw=">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</latexit><latexit sha1_base64="ej+Zqym94J2bLRdWdgCmXh+Grcw=">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</latexit><latexit sha1_base64="7m4LpSlx62Q1kiBqyil8YmoS5ts=">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</latexit>
ˆ⇢1<latexit sha1_base64="kqTr6MI4cG3iH3U2fgdpBtGjZ3c=">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</latexit><latexit sha1_base64="kqTr6MI4cG3iH3U2fgdpBtGjZ3c=">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</latexit><latexit sha1_base64="kqTr6MI4cG3iH3U2fgdpBtGjZ3c=">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</latexit><latexit sha1_base64="0SH3hpsRHWfV2rGCw8YFRpfxZUU=">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</latexit>
ˆ⇢2<latexit sha1_base64="OLTRd2GD1IzM6aRlmZBuYE3fMx0=">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</latexit><latexit sha1_base64="OLTRd2GD1IzM6aRlmZBuYE3fMx0=">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</latexit><latexit sha1_base64="OLTRd2GD1IzM6aRlmZBuYE3fMx0=">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</latexit><latexit sha1_base64="t4w436/XDJ/IeVeYAOMDjCHFSbg=">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</latexit>
- measured density matrix
- theoretical density matrix
Classical best
strategy:
| i = cos(✓/2)|0i + ei
sin(✓/2)|1i<latexit sha1_base64="2gSt+2FTbwDNWeis11lOfXjIqq4=">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</latexit><latexit 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For a general qubit state:
ˆ⇢2 = | ih | =
✓
cos2
(✓/2) e i
sin(✓/2) cos(✓/2)
ei
sin(✓/2) cos(✓/2) sin2
(✓/2)
◆
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Averaged measurements in the eigenbasis of
ˆ⇢1 =
✓
cos2
(✓/2) 0
0 sin2
(✓/2)
◆
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ˆZ<latexit sha1_base64="lxldWAwsdPglvM5xwvcKi9C9RhE=">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</latexit><latexit sha1_base64="lxldWAwsdPglvM5xwvcKi9C9RhE=">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</latexit><latexit sha1_base64="lxldWAwsdPglvM5xwvcKi9C9RhE=">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</latexit><latexit sha1_base64="fadpcYRvaKeeZtnqIy8qwMC0Mek=">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</latexit>
F(⇢1, ⇢2) = cos4
(✓/2) + sin4
(✓/2)<latexit sha1_base64="J0yWTm1TxYuYSwfNBGUBRodtE5E=">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</latexit><latexit sha1_base64="J0yWTm1TxYuYSwfNBGUBRodtE5E=">AAAC+XicjVHdShwxGD2O1p/1b2svvRlchF1a1pllQW8KYqF4acFdBUeXmRjd4OxkSDKCLL6Id96Jt32B3tYXEN9A36Jf4gi2S9EMk5yc7zsn+fIleSq0CYKHMW984sPk1PRMZXZufmGx+nGpq2WhGO8wmUq1n8SapyLjHSNMyvdzxeNBkvK95Oybje+dc6WFzHbNRc4PB/FpJk4Eiw1RvWr7ez1SfdkLv7il1fC/+hGT+qhdj0yfm3it1fgcaZG9JnrVWtAM3PBHQViCGsqxI6v3iHAMCYYCA3BkMIRTxND0HSBEgJy4QwyJU4SEi3NcokLagrI4ZcTEntF8SruDks1obz21UzM6JaVfkdLHKmkk5SnC9jTfxQvnbNn/eQ+dp73bBa1J6TUg1qBP7Fu6l8z36mwtBifYcDUIqil3jK2OlS6FexV7c/9VVYYccuIsPqa4Isyc8uWdfafRrnb7trGLP7pMy9o9K3MLPNlbUoPDf9s5CrqtZhg0wx/t2uZW2eppLGMFdernOjaxjR10yPsKv/Abd97Qu/ZuvNvnVG+s1HzCX8P7+QdjMaG9</latexit><latexit sha1_base64="J0yWTm1TxYuYSwfNBGUBRodtE5E=">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</latexit><latexit sha1_base64="5t3slGw3kvod/reEEgOGLcj13yE=">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</latexit>
for which the fidelity is
Since the state is unknow, averaging over the Bloch sphere
has to done, which yields:
1
4⇡
Z
4⇡
F(⇢1, ⇢2)d⌦ =
2
3
.
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allow to find
the density matrix is
Finding F=2/3.
Bose-Einstein Condensate in Space arXiv:1806.06679
``We emphasise that our experiments already demonstrate the tools
of atom optics required by satellite gravimetry, quantum tests of the
Equivalence principle and gravitational wave detection based on
matter-wave interferometry in space. Moreover, they pave the way to
miniaturise cold-atom and photon-based quantum information
concepts, and integrate them into quantum-communication satellites,
making the quantum internet a reality.’’
Perspectives
Satelitary quantum internet - QKD on intercontinental
distances
New way to test interplay between gravitational
and quantum physics (relativistic quantum information
theory, quantum fields on curved backgrounds, BEC,..)
Development of CubeSats devoted to QKD and quantum
physics experiments.
Quantum information processing in space.
Applications to: gravimetry, precise distance measurements,
gravitational wave astronaomy, …
Thank you!
Future - Quantum information
processing in space
High vacuum + low temperature
> reduction of quantum decoherence
Lunar (Quantum) Computing/Data Centre?
scales not preserved!
The tidal locking matters! There can
be a communication station on the Moon
directed towards the Earth.

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Quantum Space Technologies

  • 2. Photons - quanta of light Horizontal polarization Vertical polarization CC BY-3.0 |Hi = |0i<latexit sha1_base64="C15KgnNZsU6a8emn0b4SLSwwr00=">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</latexit><latexit sha1_base64="C15KgnNZsU6a8emn0b4SLSwwr00=">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</latexit><latexit sha1_base64="C15KgnNZsU6a8emn0b4SLSwwr00=">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</latexit><latexit sha1_base64="/ORkbi8ycvVeRgA96el/WocjQ9s=">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</latexit> |V i = |1i<latexit sha1_base64="z0F4Em0l+qSkDByc8LczO63xTyE=">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</latexit><latexit sha1_base64="z0F4Em0l+qSkDByc8LczO63xTyE=">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</latexit><latexit sha1_base64="z0F4Em0l+qSkDByc8LczO63xTyE=">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</latexit><latexit sha1_base64="kOaz2q6ekYexSM32zcee3Fh71WA=">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</latexit> state state
  • 3. | i = cos(✓/2)|0i + ei sin(✓/2)|1i<latexit sha1_base64="2gSt+2FTbwDNWeis11lOfXjIqq4=">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</latexit><latexit 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sha1_base64="/RKKLTVSQdlFkB/lm43n5vKj+mI=">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</latexit> In general, photon is in quantum superposition of the two polarizations: Quantum state of a photon is an example of a qubit (quantum bit). CC BY-SA 3.0 Photon Qubit This is due to the fact that photon is a masless spin 1 particle with two helicity states: |Li = 1 p 2 (|0i i|1i) <latexit sha1_base64="PmUBFBQXOBPefRWJxOnw+7aB7eg=">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</latexit><latexit 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  • 4. |Ri<latexit sha1_base64="glVsbgHZCyGulJ3A3/JpH9JWsKY=">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</latexit><latexit 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  • 5. Quantum key distribution - QKD No-cloning theorem - an unknown state can’t be copied. Distrobution of private key utilizing quantum bits and fundamental properties of quantum mechanics: Measusrement reduce a quantum state. Mehic, M., Maurhart, O., Rass, S. et al. Quantum Inf Process (2017) 16: 253
  • 6. No-cloning of qubits | i = ↵|0i + |1i<latexit sha1_base64="KnjSa2qv+IpETeXL6+1Kh1Ctio4=">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</latexit><latexit 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sha1_base64="PURkbTB2QPwPjzeIWLcco5jcik8=">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</latexit> We would like to copy an unknown state ˆC(| i ⌦ | i) = | i ⌦ | i<latexit 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sha1_base64="MBnsbeGh+PaIk5YNi+Fyxiqy1v0=">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</latexit><latexit 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sha1_base64="CVZYbJL/WOz+KKsp+t2TXR2jkWM=">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</latexit><latexit sha1_base64="XSUYELRRaosTU5WWGMt3lWnoTQg=">AAADC3icjVHLSsNAFD3GV31XXboJFkE3JXGjG6FYEJcVrApGZBLHdjAvJhNBWj/BP3HnTtz6A25E9AP0L7wzpqIW0QlJzpx7zpm5M34aikw5ztOANTg0PDJaGhufmJyaninPzu1lSS4D3gySMJEHPst4KGLeVEKF/CCVnEV+yPf9s7qu759zmYkk3lUXKT+KWCsWpyJgiqjj8pbXZqpTv1zuOrYnWdwKue0lSkQ8s7teoy167MpG1+kTfHqOyxWn6phh9wO3ABUUo5GUH+HhBAkC5IjAEUMRDsGQ0XMIFw5S4o7QIU4SEqbOcYlx8uak4qRgxJ7Rt0Wzw4KNaa4zM+MOaJWQXklOG0vkSUgnCevVbFPPTbJmf8vumEy9twv6+0VWRKxCm9i/fD3lf326F4VTrJseBPWUGkZ3FxQpuTkVvXP7S1eKElLiND6huiQcGGfvnG3jyUzv+myZqb8apWb1PCi0Od70LumC3Z/X2Q/2VquuU3V3Viu1zeKqS1jAIpbpPtdQwzYaaFL2NR7wjBfryrqxbq27D6k1UHjm8W1Y9+/5w6tT</latexit> ˆC(|1i ⌦ | i) = |1i ⌦ |1i<latexit sha1_base64="M5B+B1V26f4JSp9qkb28/DRUnRs=">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</latexit><latexit sha1_base64="M5B+B1V26f4JSp9qkb28/DRUnRs=">AAADC3icjVHLSsQwFD3W9/gademmOAi6GVoRdCOIgrgcwRkFK5LWOBPsizQVZMZP8E/cuRO3/oAbEf0A/QtvYkfUQTSl7cm555zkJn4aikw5zlOf1T8wODQ8MloaG5+YnCpPzzSyJJcBrwdJmMgDn2U8FDGvK6FCfpBKziI/5Pv+2Zau759zmYkk3lMXKT+KWDMWpyJgiqjj8rbXYqq9dbnYcW1PsrgZcttLlIh4Zne8Wkt02aX1jtsj+PQclytO1THD7gVuASooRi0pP8LDCRIEyBGBI4YiHIIho+cQLhykxB2hTZwkJEyd4xIl8uak4qRgxJ7Rt0mzw4KNaa4zM+MOaJWQXklOGwvkSUgnCevVbFPPTbJmf8tum0y9twv6+0VWRKxCi9i/fF3lf326F4VTrJkeBPWUGkZ3FxQpuTkVvXP7S1eKElLiND6huiQcGGf3nG3jyUzv+myZqb8apWb1PCi0Od70LumC3Z/X2Qsay1XXqbq7K5WNzeKqRzCHeSzSfa5iAzuooU7Z13jAM16sK+vGurXuPqRWX+GZxbdh3b8DAfCrWA==</latexit><latexit sha1_base64="M5B+B1V26f4JSp9qkb28/DRUnRs=">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</latexit><latexit sha1_base64="ajI2UaLW8pP3N0Z+Tbtvo6zJbUA=">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</latexit> Acting on the basis states we obtain: With the use of linearity of the operator ˆC<latexit sha1_base64="jjWc3ChqFbg97FASrFK6HzXmHTY=">AAACynicjVHLSsNAFD2Nr1pfVZdugkVwVRIRdFnsxoWLCvYBtsgknbahaRImE6GE7vwBt/ph4h/oX3hnnIJaRCckOXPuOXfm3uslYZBKx3ktWEvLK6trxfXSxubW9k55d6+VxpnwedOPw1h0PJbyMIh4UwYy5J1EcDbxQt72xnUVb99zkQZxdCOnCe9N2DAKBoHPJFHt7ojJvD67K1ecqqOXvQhcAyowqxGXX9BFHzF8ZJiAI4IkHIIhpecWLhwkxPWQEycIBTrOMUOJvBmpOCkYsWP6Dml3a9iI9ipnqt0+nRLSK8hp44g8MekEYXWareOZzqzY33LnOqe625T+nsk1IVZiROxfvrnyvz5Vi8QA57qGgGpKNKOq802WTHdF3dz+UpWkDAlxCvcpLgj72jnvs609qa5d9Zbp+JtWKlbtfaPN8K5uSQN2f45zEbROqq5Tda9PK7ULM+oiDnCIY5rnGWq4RANNXeUjnvBsXVnCmlr5p9QqGM8+vi3r4QPw3ZIV</latexit><latexit sha1_base64="jjWc3ChqFbg97FASrFK6HzXmHTY=">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</latexit><latexit sha1_base64="jjWc3ChqFbg97FASrFK6HzXmHTY=">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</latexit><latexit sha1_base64="SD4FtEdYrr4dzl3QW5YZMi+u4o0=">AAACynicjVHLTsJAFD3UF+ILdemmkZi4Ii0bXRLZuHCBiYAJEDMtA0wobTOdmpCGnT/gVj/M+Af6F94ZS6ISo9O0PXPuOXfm3uvFgUiU47wWrJXVtfWN4mZpa3tnd6+8f9BOolT6vOVHQSRvPZbwQIS8pYQK+G0sOZt6Ae94k4aOd+65TEQU3qhZzPtTNgrFUPhMEdXpjZnKGvO7csWpOmbZy8DNQQX5akblF/QwQAQfKabgCKEIB2BI6OnChYOYuD4y4iQhYeIcc5TIm5KKk4IRO6HviHbdnA1pr3Mmxu3TKQG9kpw2TsgTkU4S1qfZJp6azJr9LXdmcuq7zejv5bmmxCqMif3Lt1D+16drURji3NQgqKbYMLo6P8+Smq7om9tfqlKUISZO4wHFJWHfOBd9to0nMbXr3jITfzNKzeq9n2tTvOtb0oDdn+NcBu1a1XWq7nWtUr/IR13EEY5xSvM8Qx2XaKJlqnzEE56tK0taMyv7lFqF3HOIb8t6+ADwPZIT</latexit> we find ˆC(| i ⌦ | i) = ↵|0i ⌦ |0i + |1i ⌦ |1i<latexit sha1_base64="M5gMVuXuLjnJKHjYIyoyFxH6J98=">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</latexit><latexit sha1_base64="M5gMVuXuLjnJKHjYIyoyFxH6J98=">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</latexit><latexit sha1_base64="M5gMVuXuLjnJKHjYIyoyFxH6J98=">AAADPHicjVHLSgMxFL0zvmp9VV26CRZBEcqMCLoRxG5cVrBa6EjJjLENZh4kGUWqv+ZviAt3LhRx69qbOBW1iGaYmZNzzznJTcJMcKU9795xR0bHxidKk+Wp6ZnZucr8wpFKcxmxZpSKVLZCqpjgCWtqrgVrZZLROBTsODyvm/rxBZOKp8mhvsrYSUy7CT/jEdVIdSqXQY/qfv1m9TpoKE4CSZOuYCRINY+ZIsj2Ptk1skMCKrIeJdfekNL7NK+TIGQaRf6QyB+IOpWqV/PsIMPAL0AVitFIK3cQwCmkEEEOMTBIQCMWQEHh0wYfPMiQO4E+chIRt3UGN1BGb44qhgqK7Dl+uzhrF2yCc5OprDvCVQS+Ep0EVtCTok4iNqsRW89tsmF/y+7bTLO3K/yHRVaMrIYesn/5Bsr/+kwvGs5g2/bAsafMMqa7qEjJ7amYnZMvXWlMyJAz+BTrEnFknYNzJtajbO/mbKmtP1mlYc08KrQ5PJtd4gX7P69zGBxt1Hyv5h9sVnf3iqsuwRIswyre5xbswj40oInZD86IM+3MuLfuo/vivn5IXafwLMK34b69A315uzA=</latexit><latexit sha1_base64="eRCboPPMzoPslZipbOUI1GR/kSo=">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</latexit> while the expected product state should be | i ⌦ | i = ↵2 |0i ⌦ |0i + ↵ (|0i ⌦ |1i + |1i ⌦ |0i) + 2 |1i ⌦ |1i<latexit sha1_base64="cTZfPJHc3vKlBvRkjjG+2w+q2Ng=">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</latexit><latexit sha1_base64="cTZfPJHc3vKlBvRkjjG+2w+q2Ng=">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</latexit><latexit sha1_base64="cTZfPJHc3vKlBvRkjjG+2w+q2Ng=">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</latexit><latexit sha1_base64="j/1zZbkvjWzcJawbRaWDYU0uLuo=">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</latexit> The proof can easily be extended to any state | i<latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="/TMCn7Xyy44eDQTP/RuL94TJ5DE=">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</latexit>
  • 7. BB84 QKD protocol B1 = {|0i, |1i}<latexit sha1_base64="3T/6D30Fp2j7qoCySq5qgK1Dejg=">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</latexit><latexit sha1_base64="3T/6D30Fp2j7qoCySq5qgK1Dejg=">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</latexit><latexit sha1_base64="3T/6D30Fp2j7qoCySq5qgK1Dejg=">AAAC83icjVHLTtwwFD2klFcLpO2SjcWoUhdVlCAk2CAh2HRJJQaQCBo5xsxE4zzkOEijMH/RHTvEtj/QbfsPVf+g/AXXJiPxEAJHSY7PvefY996kVGllwvDflPdm+u3M7Nz8wrv3i0vL/oePB1VRayG7olCFPkp4JVWay65JjZJHpZY8S5Q8TIa7Nn54LnWVFvm+GZXyJOP9PD1LBTdE9fwgzrgZCK6anXEvYlssbtgFC1msed5X8usFiyaYsXjc8zthELrFnoKoBR20a6/w/yLGKQoI1MggkcMQVuCo6DlGhBAlcSdoiNOEUheXGGOBtDVlScrgxA7p26fdccvmtLeelVMLOkXRq0nJ8Jk0BeVpwvY05uK1c7bsc96N87R3G9E/ab0yYg0GxL6km2S+VmdrMTjDpqshpZpKx9jqROtSu67Ym7N7VRlyKImz+JTimrBwykmfmdNUrnbbW+7i/12mZe1etLk1buwtacDR43E+BQdrQRQG0ff1zvZOO+o5rGAVX2ieG9jGN+yhS94/8Au/8cervUvvyru+S/WmWs0nPFjez1senKA0</latexit><latexit sha1_base64="6CGaZj0NBNNHJn++ArEpA9C7jpg=">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</latexit> Let us consider two mutually unbiased bases: B2 = {|+i, | i}<latexit sha1_base64="kkYJKc78j+S4MO58nmsNnOKtE6g=">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</latexit><latexit sha1_base64="kkYJKc78j+S4MO58nmsNnOKtE6g=">AAAC83icjVHLattAFD1W0zzcJnGbZTdDTaHQxkghkG4KId1kmUL9AMuY0XjsiIwejEYFY/svuuuudNsfyDb5h5A/SP6id6YypDWlHSHpzLn3nJl7b5SruDC+f1vzHq09Xt/Y3Ko/ebq9s9t49rxTZKUWsi0ylelexAup4lS2TWyU7OVa8iRSshtdfLDx7mepizhLP5lpLgcJn6TxOBbcEDVstMKEm3PB1exkMTxg71k4Y3P2hoWapxMl387Z/hIzFi6Gjabf8t1iqyCoQBPVOssaNwgxQgaBEgkkUhjCChwFPX0E8JETN8CMOE0odnGJBeqkLSlLUgYn9oK+E9r1KzalvfUsnFrQKYpeTUqGV6TJKE8TtqcxFy+ds2X/5j1znvZuU/pHlVdCrME5sf/SLTP/V2drMRjjnashpppyx9jqROVSuq7Ym7MHVRlyyImzeERxTVg45bLPzGkKV7vtLXfxO5dpWbsXVW6Je3tLGnDw5zhXQeegFfit4ONh8/ikGvUmXuAlXtM8j3CMU5yhTd5fcIkrXHul99X75n3/lerVKs0eflvej58LFaAs</latexit><latexit sha1_base64="kkYJKc78j+S4MO58nmsNnOKtE6g=">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</latexit><latexit sha1_base64="fSOglpW4eeTXdyXiH3YGRxu6Xso=">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</latexit> and so that |h | i|2 = 1 2<latexit sha1_base64="5aZ5R3OMQrGuXC6UjyVhDyohZtE=">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</latexit><latexit sha1_base64="5aZ5R3OMQrGuXC6UjyVhDyohZtE=">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</latexit><latexit sha1_base64="5aZ5R3OMQrGuXC6UjyVhDyohZtE=">AAAC83icjVHBbtNAEH1xoS2FllCOXFZESJwiO6pULkhRe+mxSKSNFKfRerNJVtnY1nqNFCX5i964Vb32B7jCPyD+AP6C2cWRgAjRtWy/eTPv7c5OkmtV2DD8Vgu2Hjzc3tl9tPf4yf7B0/qzw4siK42QHZHpzHQTXkitUtmxymrZzY3ks0TLy2R66vKXH6QpVJa+t/Nc9md8nKqREtwSNag3lyzWPB1ryeJ8ohiFeaFYbDy3vGqxtyweGS4W0WrRWg3qjbAZ+sU2QVSBBqp1ntW/IsYQGQRKzCCRwhLW4Cjo6SFCiJy4PhbEGULK5yVW2CNtSVWSKjixU/qOKepVbEqx8yy8WtAuml5DSoZXpMmozhB2uzGfL72zY//lvfCe7mxz+ieV14xYiwmx/9OtK++rc71YjPDG96Cop9wzrjtRuZT+VtzJ2W9dWXLIiXN4SHlDWHjl+p6Z1xS+d3e33Oe/+0rHulhUtSV+uFPSgKO/x7kJLlrNKGxG744a7ZNq1Lt4gZd4TfM8RhtnOEeHvK/xCZ/xJSiDj8FNcPurNKhVmuf4YwV3PwHKBKFN</latexit><latexit sha1_base64="/XVgK3pu4kRwHKeC1zQyCe3yLp0=">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</latexit> 8 | i 2 B1<latexit 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sha1_base64="kmgOcCfjDFin7Tt0N71ugSul2pg=">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</latexit> Sender (Alice) is randomly choosing between the 4 polarization states to generate the secret key.
  • 8. Reciever (Bob) analyses the photon states in one of the two bases, withouth the prior knowledge of the polarization bases used by Alice. Using a classical channel, Bob announces his measurement bases. Basis reconciliation is made at this point. The last step is to verify if no attack has been made. 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  • 9. A simple uncorrelated attack An eavesdropper (Eve) does not know what the bases chosen by Alice are. How probable is that Eve is not detected? 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sha1_base64="hSEIIgRPV9ZlMw8gy8h76qzzJeI=">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</latexit><latexit sha1_base64="hSEIIgRPV9ZlMw8gy8h76qzzJeI=">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</latexit><latexit sha1_base64="hSEIIgRPV9ZlMw8gy8h76qzzJeI=">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</latexit><latexit sha1_base64="OemnERYvuN/EPX2HkxZBlqH/cC8=">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</latexit> 1<latexit sha1_base64="nY8hzPj3CKCZuv3SM159RUZ0WgQ=">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</latexit><latexit sha1_base64="nY8hzPj3CKCZuv3SM159RUZ0WgQ=">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</latexit><latexit sha1_base64="nY8hzPj3CKCZuv3SM159RUZ0WgQ=">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</latexit><latexit sha1_base64="XPupLPfcVGDyo5uXnY6ujO9GvVU=">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</latexit> Bob (B) The probability is: P(0) = 1 2 · 1 + 1 2 · 1 2 = 3 4<latexit sha1_base64="2UEwVMutiXvb+VxrvhnJcc4YjWk=">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</latexit><latexit sha1_base64="2UEwVMutiXvb+VxrvhnJcc4YjWk=">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</latexit><latexit sha1_base64="2UEwVMutiXvb+VxrvhnJcc4YjWk=">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</latexit><latexit sha1_base64="eRrrjHtLf4XZI6WEMzIm3x1R3HY=">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</latexit> ✓ 3 4 ◆N <latexit sha1_base64="Pz+32BHmq47boE2SZUoBPpL5TGk=">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</latexit><latexit sha1_base64="Pz+32BHmq47boE2SZUoBPpL5TGk=">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</latexit><latexit sha1_base64="Pz+32BHmq47boE2SZUoBPpL5TGk=">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</latexit><latexit sha1_base64="n060Tdg65Ore6BH3Ry/iknwRFrE=">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</latexit> For N bits:
  • 10. QBER - Quantum Bit Error Rate QBER (e) - error rate per qubit qubits with error number of qubits e := Ne N<latexit sha1_base64="vylH4oT7wuFf9eDE4LMrMATRaxc=">AAAC2XicjVHLSsNAFD2Nr1pf8bFzEyyCq5KIoAhC0Y2rUsG2QpWSjFMNpkmYTIQasnAnbv0Bt/pD4h/oX3hnjOAD0QlJzpx7z5m593px4CfStp9Lxsjo2PhEebIyNT0zO2fOL7STKBWMt1gUROLIcxMe+CFvSV8G/CgW3B14Ae94F3sq3rnkIvGj8FAOY34ycM9Cv+8zVxLVM5e4tb1jHfeFy7JGL+N5njXynlm1a7Ze1k/gFKCKYjUj8wnHOEUEhhQDcISQhAO4SOjpwoGNmLgTZMQJQr6Oc+SokDalLE4ZLrEX9D2jXbdgQ9orz0SrGZ0S0CtIaWGVNBHlCcLqNEvHU+2s2N+8M+2p7jakv1d4DYiVOCf2L91H5n91qhaJPrZ0DT7VFGtGVccKl1R3Rd3c+lSVJIeYOIVPKS4IM6386LOlNYmuXfXW1fEXnalYtWdFbopXdUsasPN9nD9Be73m2DXnYKNa3y1GXcYyVrBG89xEHftookXeV7jHAx6NrnFt3Bi376lGqdAs4ssy7t4AaRiXUA==</latexit><latexit sha1_base64="vylH4oT7wuFf9eDE4LMrMATRaxc=">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</latexit><latexit sha1_base64="vylH4oT7wuFf9eDE4LMrMATRaxc=">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</latexit><latexit sha1_base64="WNnJp9g33+9rN4RtmGWNFMPShnA=">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</latexit> In the case of uncorrelated attack on BB84 e = f 4<latexit sha1_base64="aT37GPn+dcFAsV7a2eR79ixMjWQ=">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</latexit><latexit sha1_base64="aT37GPn+dcFAsV7a2eR79ixMjWQ=">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</latexit><latexit sha1_base64="aT37GPn+dcFAsV7a2eR79ixMjWQ=">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</latexit><latexit sha1_base64="AFOwIQWSuI69RF6zAztIq60IAlA=">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</latexit> f<latexit sha1_base64="7QQfQx4iNX04F8go9Nvv8s3hbAI=">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</latexit><latexit sha1_base64="7QQfQx4iNX04F8go9Nvv8s3hbAI=">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</latexit><latexit sha1_base64="7QQfQx4iNX04F8go9Nvv8s3hbAI=">AAACxHicjVHLSsNAFD2Nr1pfVZdugkVwVRIRdFkUxGUL9gG1SDKd1qHTJGQmQin6A27128Q/0L/wzpiCWkQnJDlz7j1n5t4bJlIo7XmvBWdhcWl5pbhaWlvf2Nwqb++0VJyljDdZLOO0EwaKSxHxphZa8k6S8mAcSt4OR+cm3r7jqRJxdKUnCe+Ng2EkBoIFmqjG4KZc8aqeXe488HNQQb7qcfkF1+gjBkOGMTgiaMISARQ9XfjwkBDXw5S4lJCwcY57lEibURanjIDYEX2HtOvmbER746msmtEpkt6UlC4OSBNTXkrYnObaeGadDfub99R6mrtN6B/mXmNiNW6J/Us3y/yvztSiMcCprUFQTYllTHUsd8lsV8zN3S9VaXJIiDO4T/GUMLPKWZ9dq1G2dtPbwMbfbKZhzZ7luRnezS1pwP7Pcc6D1lHV96p+47hSO8tHXcQe9nFI8zxBDZeoo2m9H/GEZ+fCkY5yss9Up5BrdvFtOQ8fQFyPaw==</latexit><latexit sha1_base64="gW0ua91YbXX5ZKtY6q81l7g764Y=">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</latexit> - fraction of qubits analyzed by Eve (E) Shannon entropy per bit h(e) = e log(e) (1 e) log(1 e)<latexit sha1_base64="uj+6jDBVdaoVyWMQudtXgVfcLGQ=">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</latexit><latexit sha1_base64="uj+6jDBVdaoVyWMQudtXgVfcLGQ=">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</latexit><latexit sha1_base64="uj+6jDBVdaoVyWMQudtXgVfcLGQ=">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</latexit><latexit sha1_base64="zPuvMWRyiJ1652Plml4Qtz6wRE4=">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</latexit> I(A : B) = 1 h(e)<latexit sha1_base64="PB1XmOXxRLEkKzTi6Qx6CbQu7ok=">AAAC0HicjVHLSsNAFD2Nr1pfVZdugkVoF5ZEBEUQat3orop9QC2STKc1NE1iMhFLEXHrD7jVrxL/QP/CO2MKahGdkOTMufecmXuvHbhOJAzjNaVNTE5Nz6RnM3PzC4tL2eWVWuTHIeNV5rt+2LCtiLuOx6vCES5vBCG3+rbL63bvUMbr1zyMHN87E4OAt/pW13M6DrMEUa3j/MFeubBvbl7meeEimzOKhlr6ODATkEOyKn72BedowwdDjD44PAjCLixE9DRhwkBAXAtD4kJCjopz3CJD2piyOGVYxPbo26VdM2E92kvPSKkZneLSG5JSxwZpfMoLCcvTdBWPlbNkf/MeKk95twH97cSrT6zAJbF/6UaZ/9XJWgQ62FU1OFRToBhZHUtcYtUVeXP9S1WCHALiJG5TPCTMlHLUZ11pIlW77K2l4m8qU7Jyz5LcGO/yljRg8+c4x0Ftq2gaRfNkO1cqJ6NOYw3ryNM8d1DCESqokvcVHvGEZ+1Uu9HutPvPVC2VaFbxbWkPH2wDko0=</latexit><latexit 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sha1_base64="PB1XmOXxRLEkKzTi6Qx6CbQu7ok=">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</latexit><latexit sha1_base64="94dCv2yFWLg9WuIEDCzLkfCfIfE=">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</latexit> Mutual information between A and B: Mutual information between A and E: I(A : E) = f/2 = 2e<latexit sha1_base64="pWLLOiuZZklOFWFiDTu6dFmG/es=">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</latexit><latexit sha1_base64="pWLLOiuZZklOFWFiDTu6dFmG/es=">AAAC0XicjVHLSsNAFD2Nr1pfVZdugkWom5oUQREKVRF0V9E+oFZJ0mkNTZMwmQilCOLWH3CrPyX+gf6Fd8YU1CI6IcmZc+85M/deO/TcSBjGa0qbmJyanknPZubmFxaXsssrtSiIucOqTuAFvGFbEfNcn1WFKzzWCDmz+rbH6nbvUMbrN4xHbuCfi0HIWn2r67sd17EEUZcn+f29o81SZ6tYKjL9KpszCoZa+jgwE5BDsipB9gUXaCOAgxh9MPgQhD1YiOhpwoSBkLgWhsRxQq6KM9wiQ9qYshhlWMT26NulXTNhfdpLz0ipHTrFo5eTUscGaQLK44TlabqKx8pZsr95D5WnvNuA/nbi1SdW4JrYv3SjzP/qZC0CHeyqGlyqKVSMrM5JXGLVFXlz/UtVghxC4iRuU5wTdpRy1GddaSJVu+ytpeJvKlOycu8kuTHe5S1pwObPcY6DWrFgGgXzdDtXPkhGncYa1pGnee6gjGNUUCVvjkc84Vk70wbanXb/maqlEs0qvi3t4QMyWpLZ</latexit><latexit sha1_base64="pWLLOiuZZklOFWFiDTu6dFmG/es=">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</latexit><latexit sha1_base64="IEXRH8VSgmSZnliyppQniZxZ72M=">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</latexit> If I(A : E) I(A : B)<latexit sha1_base64="G+lfmHLoFrDm1HBRuMree2cROrg=">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</latexit><latexit sha1_base64="G+lfmHLoFrDm1HBRuMree2cROrg=">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</latexit><latexit sha1_base64="G+lfmHLoFrDm1HBRuMree2cROrg=">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</latexit><latexit sha1_base64="BKF7BURvBNjRRUDyLQAXlyTNFPk=">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</latexit> then E has more information than B, which is when e & 17 %<latexit sha1_base64="BnLo/j4jA7Zz4b9ocFMo6q7lAxY=">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</latexit><latexit 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sha1_base64="BnLo/j4jA7Zz4b9ocFMo6q7lAxY=">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</latexit><latexit sha1_base64="HGZ6HTCy1YzGiTL5Kp6r1IMtd1M=">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</latexit>
  • 11. Limitations on distance due to losses in optical fiber… QKD is already in commercial use The signal may be amplified with the use quantum repeaters www.cqc2t.org
  • 12. Exponential suppression of photons with distance in the fiber. Possible solution: Inverse-square suppression of photons in vacuum… Recently even 10 Mb/s in fiber (arXiv: 1807.04484) ~ 1 Mb/s over 50 km of standard optical fibre ~ 1 bit per hour over 400 kilometres of ultralow-loss fibre
  • 13. Intercontinental QKD - Chinese Micius satellite (2017). It is much easier to transmit quantum signal in air/vacuum. arXiv:1801.04418 ~ 3 kb/s at ~1000 km ~ 9 kb/s at ~600 km
  • 14. XINHUA / JIN LIWANG / MCG
  • 15. Quantum encrypted one-time-pad file transfer. Video transfer encrypted with the use Advanced Encryption Standard (AES) -192. A new 192 bit quantum distributed key has been provided every second. arXiv:1801.04418
  • 16. Space based QKD configurations R. Bendington et al. EPJ Quantum Technology (2016) 3:12
  • 20. Ekert (E91) protocol | ABi = 1 p 2 (|0iA|0iB + |1iA|1iB) = 1 p 2 (|✓iA|✓iB + |✓?iA|✓?iB) <latexit sha1_base64="dEM4ehyGybv1R87Cla/wgkzSeQw=">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</latexit><latexit sha1_base64="dEM4ehyGybv1R87Cla/wgkzSeQw=">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</latexit><latexit sha1_base64="dEM4ehyGybv1R87Cla/wgkzSeQw=">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</latexit><latexit sha1_base64="pbvgud4TGvxrHohqiWrqbphdqcg=">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</latexit> EPR pairs are created between Alice (A) and Bob (B): Security is confirmed by virtue of the Bell’s inequality. arXiv:1406.1685
  • 21. SPEQS (Small Photon-Entangling Quantum System) arXiv:1603.06659
  • 23. SpooQySat R. Bendington et al. EPJ Quantum Technology (2016) 3:12
  • 24. Nanobob - CubeSat 12U (quantum uplink only) Q3Sat - CubeSat 3U (quantum uplink only) arXiv:1711.01886 EPJ Quantum Technology (2018) 5:4
  • 25. Activated Entangled Photon Source www.fraunhofer.de
  • 26. Passive photon exchange with GNSS arXiv:1804.05022 Exchange of single photons by exploiting retroreflector array mounted on GLONASS satellites. The first exchange of a few photons per pulse along a channel length of 20000 km, reaching a SNR about 0.5 and a detection rate around 60 Hz.
  • 27. Effects of General Relativity QFT in Schwarzschild metric QFT in Kerr metric Curvedspacetime arXiv:1309.3088 QBER ⇠ 2 ⌦2 B,0 8 2 ⇠ 0.7% <latexit sha1_base64="6+7E6vPkc1zZ8LNLmjObJeztU14=">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</latexit><latexit 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sha1_base64="FavJWh22ihiJDPkSmc/3i51gvOA=">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</latexit> arXiv:1409.0234 arXiv:1511.04256 QBER ⇠ 10 2 (GEO)<latexit 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sha1_base64="Vn8F6Tn4iWMtn7VJmyVGNqS6bL8=">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</latexit> QBER ⇠ 10 4 (LEO)<latexit sha1_base64="RmCojH7SQhr8ZjI9r4SfPWaQcF0=">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</latexit><latexit 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sha1_base64="8wfK7Xt4bpUm0WgMDIPRtJEes3w=">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</latexit> QBER ⇠ 10 8 for rB ⇠ 3 2 rA <latexit sha1_base64="kDf55PUUXrYP6HYdc+gj/O49TKs=">AAADCHicjVHLLgRBFD3a+z1Y2nRMJDYm3UhYMiKxRAwSw6S71FCZfqW6Wkinf8Cf2NmJrR+wxB/wF26VlnhEqEp3n3vuObfr1vWTQKTKcZ67rO6e3r7+gcGh4ZHRsfHKxOReGmeS8QaLg1ge+F7KAxHxhhIq4AeJ5F7oB3zf76zr/P45l6mIo111mfCj0DuNRFswTxHVqqw3Fb9Q+XZ9Y6ewm6kIbdc5zudXKNDbJNuxLHQkW/V3SbMtPZYvFvlCQeRaq1J1ao5Z9k/glqCKcm3FlUc0cYIYDBlCcERQhAN4SGkfwoWDhLgj5MRJQsLkOQoMkTcjFSeFR2yH3qcUHZZsRLGumRo3o78E9Ehy2pglT0w6SVj/zTb5zFTW7G+1c1NTn+2Svn5ZKyRW4YzYv3wfyv/6dC8KbayYHgT1lBhGd8fKKpm5FX1y+1NXiiokxGl8QnlJmBnnxz3bxpOa3vXdeib/YpSa1TErtRle9SlpwO73cf4Eews116m520vV1Xo56gFMYwZzNM9lrGITW2hQ7Ws84AnP1pV1Y91ad+9Sq6v0TOHLsu7fALkWqPU=</latexit><latexit sha1_base64="kDf55PUUXrYP6HYdc+gj/O49TKs=">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</latexit><latexit sha1_base64="kDf55PUUXrYP6HYdc+gj/O49TKs=">AAADCHicjVHLLgRBFD3a+z1Y2nRMJDYm3UhYMiKxRAwSw6S71FCZfqW6Wkinf8Cf2NmJrR+wxB/wF26VlnhEqEp3n3vuObfr1vWTQKTKcZ67rO6e3r7+gcGh4ZHRsfHKxOReGmeS8QaLg1ge+F7KAxHxhhIq4AeJ5F7oB3zf76zr/P45l6mIo111mfCj0DuNRFswTxHVqqw3Fb9Q+XZ9Y6ewm6kIbdc5zudXKNDbJNuxLHQkW/V3SbMtPZYvFvlCQeRaq1J1ao5Z9k/glqCKcm3FlUc0cYIYDBlCcERQhAN4SGkfwoWDhLgj5MRJQsLkOQoMkTcjFSeFR2yH3qcUHZZsRLGumRo3o78E9Ehy2pglT0w6SVj/zTb5zFTW7G+1c1NTn+2Svn5ZKyRW4YzYv3wfyv/6dC8KbayYHgT1lBhGd8fKKpm5FX1y+1NXiiokxGl8QnlJmBnnxz3bxpOa3vXdeib/YpSa1TErtRle9SlpwO73cf4Eews116m520vV1Xo56gFMYwZzNM9lrGITW2hQ7Ws84AnP1pV1Y91ad+9Sq6v0TOHLsu7fALkWqPU=</latexit><latexit sha1_base64="ijWXi4fnEcv0PoExlDLrfJdBLTs=">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</latexit> := ⌦B ⌦A 1 = S + rot + c <latexit sha1_base64="0fffzyw9GzMFj46dRoaroEKKSgY=">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</latexit><latexit sha1_base64="0fffzyw9GzMFj46dRoaroEKKSgY=">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</latexit><latexit sha1_base64="0fffzyw9GzMFj46dRoaroEKKSgY=">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</latexit><latexit sha1_base64="YLZg2h5r9Lu9XVM49VNbsVMbQO8=">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</latexit> arXiv:1811.07322
  • 28. ESA ScyLight - SeCure and Laser Communication Technology.
  • 29. Satelitary quantum network - ,,quantum internet’’ One of the philars of the EU Quantum Flagship program. QuTech/TU Delft/Scixel
  • 30. Security of financial transactions, trading and cryptocurrencies. Secured (Earth to Earth) communication for civil and military purposes. Secured channel for telemedicne and medical data exchange. Secured comunication with satellites (military and civil). Solution to the emerging problem of insecurity of classical cryptographic systems.
  • 31. Quantum teleportation to LEO We already know how to send (teleportate) quantum information into space. This is crucial for the purpose of quantum communication. Twophotons Photon sent to space Entanglement Entanglement Photon remaining on Earth Teleported sate on Earth Teleported sate on LEO Classical channel A B | ABi = 1 p 2 (|0iA|0iB + |1iA|1iB) <latexit sha1_base64="rzJMolEr0/SGVXuApHzaNumikio=">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</latexit><latexit sha1_base64="rzJMolEr0/SGVXuApHzaNumikio=">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</latexit><latexit sha1_base64="rzJMolEr0/SGVXuApHzaNumikio=">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</latexit><latexit sha1_base64="iNNQTA8A2gvYo+n8u1nOq6XgSCM=">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</latexit> B A
  • 32. | i = ↵|0i + |1i<latexit sha1_base64="KnjSa2qv+IpETeXL6+1Kh1Ctio4=">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</latexit><latexit sha1_base64="KnjSa2qv+IpETeXL6+1Kh1Ctio4=">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</latexit><latexit sha1_base64="KnjSa2qv+IpETeXL6+1Kh1Ctio4=">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</latexit><latexit sha1_base64="PURkbTB2QPwPjzeIWLcco5jcik8=">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</latexit> In order to teleportate the state EPR pair | ABi = 1 p 2 (|0iA|0iB + |1iA|1iB) <latexit 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sha1_base64="rzJMolEr0/SGVXuApHzaNumikio=">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</latexit><latexit 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sha1_base64="iNNQTA8A2gvYo+n8u1nOq6XgSCM=">AAADNXicjVFNT9wwEJ1N+f7qAsdeLFZIIKRVspdyQVqWS49bqQtIBK0c410svEmwHSSUze/in7TqoTeE6Ik/wIGxa9RuEQJHSWbevPfs8SS5FNqE4c9a8GFqemZ2bn5hcWl55WN9de1QZ4VivMcymanjhGouRcp7RhjJj3PF6SiR/Ci5OLD1oyuutMjSb+Y656cjOkzFQDBqEOrX83Hc1aJf7neqWNF0KDnZI/FAUVZGVRnrS2XKVlXFkg/MFhmTkHhaf38i6+yMSTRR+5t1CK5YieG52Sb9eiNshm6Rl0Hkgwb41c3qPyCGM8iAQQEj4JCCwVgCBY3PCUQQQo7YKZSIKYyEq3OoYAG1BbI4MiiiF/gdYnbi0RRz66mdmuEuEl+FSgKbqMmQpzC2uxFXL5yzRV/zLp2nPds1/hPvNULUwDmib+meme/V2V4MDGDX9SCwp9whtjvmXQp3K/bk5J+uDDrkiNn4DOsKY+aUz/dMnEa73u3dUle/d0yL2px5bgG/7SlxwNH/43wZHLaaUdiMvrYa7Y4f9Rx8gg3Ywnl+hjZ8gS700Ps7PNamazPBTfAruA3u/lCDmtesw8QKHp4AXO+3qg==</latexit> is created By acting with CNOT and H gates on we obtain| i| ABi<latexit sha1_base64="qEIiw0KZ3vV8phiixZHYhwEW+DU=">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</latexit><latexit sha1_base64="qEIiw0KZ3vV8phiixZHYhwEW+DU=">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</latexit><latexit sha1_base64="qEIiw0KZ3vV8phiixZHYhwEW+DU=">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</latexit><latexit sha1_base64="pzBACqwwHB1HTYw/c117EiycHdU=">AAAC5nicjVG7TsNAEJyYVwivACWNIUKiimwaKENoKINEHlISRbY5klMc2zqfkaKQmo4O0fIDtPApiD+Av2DvcBAQITjL9uzsztztrRv5PJaW9ZIxZmbn5heyi7ml5ZXVtfz6Ri0OE+Gxqhf6oWi4Tsx8HrCq5NJnjUgwZ+D6rO72j1W+fslEzMPgTA4j1h443YBfcM+RRHXy21etSszNlnCCrs9MHXVGR+XxJ9XJF6yipZc5DewUFJCuSph/RgvnCOEhwQAMASRhHw5iepqwYSEiro0RcYIQ13mGMXKkTaiKUYVDbJ++XYqaKRtQrDxjrfZoF59eQUoTu6QJqU4QVruZOp9oZ8X+5j3SnupsQ/q7qdeAWIkesX/pJpX/1aleJC5wqHvg1FOkGdWdl7ok+lbUyc0vXUlyiIhT+JzygrCnlZN7NrUm1r2ru3V0/lVXKlbFXlqb4E2dkgZs/xznNKjtF22raJ/uF0rldNRZbGEHezTPA5Rwggqq5H2NBzziyegZN8atcfdRamRSzSa+LeP+HQCfnIA=</latexit> 1 2 |0i|0iA(↵|0iB + |0iB) + 1 2 |0i|1iA(↵|1iB + |0iB) <latexit sha1_base64="WdAfL4PsWwsbR6h5ifcmZ/8Pfmk=">AAADVHicjVFNT8JAEJ1SPxC/UI9eGpFEQ0JaYqJH1ItHTURNKCHbZYGGpW22WxMC/Ab/ncZ/oD/Amwdn15KgiLpN27dv5r3dmfEi7sfStp+NjLmwuLScXcmtrq1vbOa3tm/iMBGU1WjIQ3HnkZhxP2A16UvO7iLBSN/j7Nbrnav47T0TsR8G13IQsUafdAK/7VMikWrmH9y2IHTojIeV8ciyXUGCDmfWaIKap9aBS3jUJVPcWcn1mCRTxGFpjo/zg4/zi08zX7DLtl7WLHBSUIB0XYb5J3ChBSFQSKAPDAKQiDkQiPGpgwM2RMg1YIicQOTrOIMx5FCbYBbDDIJsD78d3NVTNsC98oy1muIpHF+BSguKqAkxTyBWp1k6nmhnxc7zHmpPdbcB/r3Uq4+shC6yf+kmmf/VqVoktOFE1+BjTZFmVHU0dUl0V9TNramqJDpEyCncwrhATLVy0mdLa2Jdu+ot0fEXnalYtadpbgKv6pY4YOf7OGfBTaXs2GXn6qhQPUtHnYVd2IMDnOcxVOECLqGG3m/GrrFvFDOPmXfTNBc/UzNGqtmBL8vc+ABkLMID</latexit><latexit 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sha1_base64="WdAfL4PsWwsbR6h5ifcmZ/8Pfmk=">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</latexit><latexit sha1_base64="SM2ov6WRDWgHSEQlFywkdxdkrpY=">AAADVHicjVHLTsJAFL2lovhGXbJpRBIMCWnZ6BJ14xITeSTWkOkwQOPQNtOpCUG+wb/T+Af6Ae5ceGcsCYqvadqeOfeeM3Pv9SLux9K2n4yMuZRdXsmtrq1vbG5t53d2W3GYCMqaNOSh6HgkZtwPWFP6krNOJBgZeZy1vZszFW/fMhH7YXApxxG7HpFB4Pd9SiRS3fy92xeETpzppDa9s2xXkGDAmXU3Q90Tq+wSHg3JHHdacT0myRxxWPnBx/nGx/nFp5sv2lVbL2sROCkoQroaYf4RXOhBCBQSGAGDACRiDgRifK7AARsi5K5hgpxA5Os4gymsoTbBLIYZBNkb/A5wd5WyAe6VZ6zVFE/h+ApUWlBCTYh5ArE6zdLxRDsr9ifvifZUdxvj30u9RshKGCL7l26W+V+dqkVCH451DT7WFGlGVUdTl0R3Rd3cmqtKokOEnMI9jAvEVCtnfba0Jta1q94SHX/WmYpVe5rmJvCibokDdr6OcxG0alXHrjoXtWL9NB11DgqwD2Wc5xHU4Rwa0ETvV6NgHBilzEPmzTTN7Edqxkg1e/BpmVvvY4zCAQ==</latexit> + 1 2 |1i|0iA(↵|0iB |0iB) + 1 2 |1i|1iA(↵|1iB |0iB) <latexit sha1_base64="YnlGP8UKLo2hV0nb+IfWdRgjH+M=">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</latexit><latexit sha1_base64="YnlGP8UKLo2hV0nb+IfWdRgjH+M=">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</latexit><latexit sha1_base64="YnlGP8UKLo2hV0nb+IfWdRgjH+M=">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</latexit><latexit sha1_base64="Xpakrh/KemvdnTYJHAWhphN1Vgc=">AAADVXicjVHJTsMwEJ207FsLHOEQUYFAiCruBY5QLhxBooDUoMoxbhvVWeQ4SKj0H/i7ij+AH+CGxNgYqSwFHCV5fjPv2TMTpCLMlOc9OoXixOTU9Mzs3PzC4lKpvLxykSW5ZLzBEpHIq4BmXIQxb6hQCX6VSk6jQPDLoHes45e3XGZhEp+ru5RfR7QTh+2QUYVUq/yw67clZX0y6NcG9y7xJY07grv3nkWtI3fbpyLt0hGuvucHXNERYmecD/nBh/zi0ypXvKpnlvsdEAsqYNdpUh6CDzeQAIMcIuAQg0IsgEKGTxMIeJAidw195CSi0MQ5DGAOtTlmccygyPbw28Fd07Ix7rVnZtQMTxH4SlS6sImaBPMkYn2aa+K5cdbsOO++8dR3u8N/YL0iZBV0kf1L95H5X52uRUEbDkwNIdaUGkZXx6xLbrqib+6OVKXQIUVO4xuMS8TMKD/67BpNZmrXvaUm/mQyNav3zObm8KxviQMmX8f5HVzUqsSrkrNa5bBuRz0Da7AB2zjPfTiEEziFBnq/OOvOprNVGBZeixPFqffUgmM1q/BpFUtvGInCPA==</latexit> If we measured |0i|0iA<latexit sha1_base64="XaWVP4uAUQH0rglAjrwXhJLn+rs=">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</latexit><latexit sha1_base64="XaWVP4uAUQH0rglAjrwXhJLn+rs=">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</latexit><latexit sha1_base64="XaWVP4uAUQH0rglAjrwXhJLn+rs=">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</latexit><latexit sha1_base64="U0EjV+Hx0CsatVUtVXPvXDFK+/E=">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</latexit> then the state of the B qubit is ↵|0iB + |1iB<latexit sha1_base64="ZSUXpchY6Cn5Ax8S8A3YtgEJM0w=">AAAC73icjVHLSsNAFD3GV31HXboZLIIolEQEXZa6cVnBasFKmcSxBqdJnEwEqf6DO3fi1h9wq38h/oH+hXfGiC9EJyQ5c+49Z+beG6QyyrTnPfU5/QODQ8OlkdGx8YnJKXd6ZidLchWKRpjIRDUDngkZxaKhIy1FM1WCdwMpdoPjDRPfPRUqi5J4W5+lYr/LO3F0GIVcE9V2l1pcpkecnTOPtRSPO1K0a8utQGjD+R8cY2237FU8u9hP4BegjGLVE/cRLRwgQYgcXQjE0IQlODJ69uDDQ0rcPnrEKUKRjQtcYJS0OWUJyuDEHtO3Q7u9go1pbzwzqw7pFEmvIiXDAmkSylOEzWnMxnPrbNjfvHvW09ztjP5B4dUlVuOI2L9075n/1ZlaNA6xbmuIqKbUMqa6sHDJbVfMzdmnqjQ5pMQZfEBxRTi0yvc+M6vJbO2mt9zGn22mYc0+LHJzvJhb0oD97+P8CXZWKr5X8bdWy9VaMeoS5jCPRZrnGqrYRB0N8r7EHe7x4Jw4V861c/OW6vQVmll8Wc7tK9tMnpo=</latexit><latexit sha1_base64="ZSUXpchY6Cn5Ax8S8A3YtgEJM0w=">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</latexit><latexit sha1_base64="ZSUXpchY6Cn5Ax8S8A3YtgEJM0w=">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</latexit><latexit sha1_base64="V5XfHfgNWdg4j8G95kR88i7Fg+I=">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</latexit> which is the teleportated version of | i<latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="a9eY7UIi42DtGBqDYUDaly1ly50=">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</latexit><latexit sha1_base64="/TMCn7Xyy44eDQTP/RuL94TJ5DE=">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</latexit> In the other cases the CNOT and Z operators have to be appllied to accomplish the teleportation protocol.
  • 33. Quantum state teleportation to Micius satellite arXiv:1707.00934
  • 34. F = 2 3<latexit sha1_base64="vwSPXvWSGOfxTEgx09U3uH9YXVc=">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</latexit><latexit 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sha1_base64="MuCDJT20me5UQCwTB1CQc0ua13Y=">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</latexit> F(⇢1, ⇢2) := tr(ˆ⇢1 ˆ⇢2)<latexit 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sha1_base64="7m4LpSlx62Q1kiBqyil8YmoS5ts=">AAAC/XicjVHLSsNAFD2Nr1pfUZdugkVoQUqSjUUQREFcVrBaaEtJ4tgG0yRMJqKU4p+4cydu/QG3uhX/QP/CO2MEtYhOSObcc+85mTvXjQM/Eab5ktPGxicmp/LThZnZufkFfXHpKIlS7rG6FwURb7hOwgI/ZHXhi4A1Ys6cvhuwY/dsV+aPzxlP/Cg8FJcxa/edbuif+p4jiOro1b1Si/eijrWuNru8udUS7EIMBB+WjFbPEQOZGHasr4FdNjp60ayYahmjwMpAEdmqRfozWjhBBA8p+mAIIQgHcJDQ04QFEzFxbQyI44R8lWcYokDalKoYVTjEntG3S1EzY0OKpWei1B79JaCXk9LAGmkiquOE5d8MlU+Vs2R/8x4oT3m2S9rdzKtPrECP2L90n5X/1cleBE5RVT341FOsGNmdl7mk6lbkyY0vXQlyiImT+ITynLCnlJ/3bChNonqXd+uo/KuqlKyMvaw2xZs8JQ3Y+jnOUXBkVyyzYh3Yxe2dbNR5rGAVJZrnBraxjxrq5H2NBzziSbvSbrRb7e6jVMtlmmV8W9r9O2V0pTw=</latexit> ˆ⇢1<latexit 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sha1_base64="0SH3hpsRHWfV2rGCw8YFRpfxZUU=">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</latexit> ˆ⇢2<latexit 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  • 35. | i = cos(✓/2)|0i + ei sin(✓/2)|1i<latexit sha1_base64="2gSt+2FTbwDNWeis11lOfXjIqq4=">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</latexit><latexit 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sha1_base64="fadpcYRvaKeeZtnqIy8qwMC0Mek=">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</latexit> F(⇢1, ⇢2) = cos4 (✓/2) + sin4 (✓/2)<latexit 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sha1_base64="/TMCn7Xyy44eDQTP/RuL94TJ5DE=">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</latexit> allow to find the density matrix is Finding F=2/3.
  • 36. Bose-Einstein Condensate in Space arXiv:1806.06679 ``We emphasise that our experiments already demonstrate the tools of atom optics required by satellite gravimetry, quantum tests of the Equivalence principle and gravitational wave detection based on matter-wave interferometry in space. Moreover, they pave the way to miniaturise cold-atom and photon-based quantum information concepts, and integrate them into quantum-communication satellites, making the quantum internet a reality.’’
  • 37. Perspectives Satelitary quantum internet - QKD on intercontinental distances New way to test interplay between gravitational and quantum physics (relativistic quantum information theory, quantum fields on curved backgrounds, BEC,..) Development of CubeSats devoted to QKD and quantum physics experiments. Quantum information processing in space. Applications to: gravimetry, precise distance measurements, gravitational wave astronaomy, …
  • 39. Future - Quantum information processing in space High vacuum + low temperature > reduction of quantum decoherence
  • 40. Lunar (Quantum) Computing/Data Centre? scales not preserved! The tidal locking matters! There can be a communication station on the Moon directed towards the Earth.