Yet another statistical analysis of the data of the ‘loophole free’ experiments of 2015 (revised)

Yet Another Statistical Analysis
of the data of the (2015)
“Loophole-Free”
Bell-CHSH Experiments
Richard D. Gill

Leiden University Combray

Mathematical Institute Causality Consultancy

http://www.math.leidenuniv.nl/~gill

http://richardgill.nl

⸘QIRIF‽ Växjö, Wednesday 12 June 2019
Combray

• Part 1

A novel “optimal” statistical data analysis of loophole-free experiments

• Part 2

Discussion: ¿ QIR - IF ?

• Part 3

Conclusion: QIR - IF
Overview
"I'm sorry I wrote you such a long letter; I didn't have time to write a short one."

Part 1
“Optimal” statistical data analysis of loophole-free experiments

I present novel statistical analyses of the data of the famous Bell-inequality experiments
of 2015 and 2016: Delft, NIST, Vienna and Munich. Every statistical analysis relies on
statistical assumptions. I’ll make the traditional, but questionable, i.i.d. assumptions.
They justify a novel (?) analysis which is both simple and (close to) optimal.
It enables us to fairly compare the results of the two main types of experiments: NIST
and Vienna CH-Eberhard “one-channel” experiment with settings and state chosen to
optimise the handling of the detection loophole (detector efficiency > 66.7%); Delft and
Munich CHSH “two channel” experiments based on entanglement swapping, with the
state and settings which achieve the Tsirelson bound (detector efficiency ≈ 100%).
One cannot say which type of experiment is better without agreeing on how to
compromise between the desires to obtain high statistical significance and high physical
significance. Moreover, robustness to deviations from traditional assumptions is also an
issue
Yet another statistical analysis of the data of the
‘loophole free’ experiments of 2015

The local polytope
• The local polytope of a 2x2x2 experiment has exactly 8
facets, A. Fine (1982).

• They are the 8 one-sided CHSH inequalities

• They are necessary and sufficient for LR.
There are no other 2x2x2 inequalities!

• CH, Eberhard, J are therefore *just* different ways
to write CHSH !

• Yet with experimental data they give different results !?
The diagram should be imagined as drawn on a plane in a higher dimensional space
The experimental data is a point close to, but not on, the plane

VIENNA data
Settings
11 12 21 22
Outcomes
dd 141.439 146.831 158.338 8.392
dn 73.391 67.941 425.067 576.445
nd 76.224 326.768 58.742 463.985
nn 875.392.736 874.976.534 875.239.860 874.651.457
Totals 875.683.790 875.518.074 875.882.007 875.700.279
Settings
11 12 21 22
Outcomes
dd 162 168 181 10
dn 84 78 485 658
nd 87 373 67 530
nn 999.668 999.381 999.267 998.802
Totals 1.000.000 1.000.000 1.000.000 1.000.000
Normaliser Normalised
1.000.000 1.000.000 1.000.000 1.000.000 1.000.000
“d” = detection, “n” = no detection
Raw counts
Normalised counts
“One channel” experiment

*Clocked* experiment: outcomes on each side are “+”,”–“, or “0”
“Two channel” experiment (CHSH - Aspect, Weihs, …, Delft, Munich)

“One channel” experiment (Clauser-Horne, Eberhard, Vienna, NIST)
Outcomes on each side are “d” corresponding to “+” and “n” corresponding to “–” or “0”

⸘ S = 2 + 4 J ‽
⸘ J = (S – 2)/4 ‽
• The experiments in Vienna and at NIST (Boulder, Colorado) do *not* use
the singlet state

• They exploit the fact that QM *can* violate CHSH from 66% detector
eﬃciency

• Clauser-Horne (1974)

• Philippe H. Eberhard (1993)

• Jan-Åke Larsson and Jason Semitecolos (1991)

• Peter Bierhorst (2016), “Geometric decompositions of Bell
polytopes with practical applications”, Journal of Physics A:
Mathematical and Theoretical
Peter Bierhorst
Philippe Eberhard
Proof !!!
(a very diﬀerent one)
Experimental mathematics !!!
Proof !!!
Jan-Åke Larsson
Jason Semitecolos

1
2/1+ rz
(31)
The two angles ni —n2 and Pi —P2 could always be
taken to be the same, or the opposite of one another, as
can be understood from an analytic study of Eqs. (10)
and (27). The vector @ turned out to be of the form
Eqs. (2)—(5).
In conclusion, it is possible to perform a loophole-free
experiment if the eKciency g of the photon counters is
higher than 66.7' and the background is less than the
value indicated on Fig. 1 for that value of g. For small
background levels, it is possible to perform a loophole-
free EPR experiment with a less than 82.8% counter ef-
B.ciency.
which can be reached in the two-photon experiment con-
sidered in this paper by first superposing states I
~I &
and I I ~& in unequal amounts,
(32)
ni = (~/2) —90', (33)
then rotating the planes of polarization of a and of b in
setup (ni, Pi) by the angles
ACKNO%'LEDG MENTS
The author is indebted to Professor R.R. Ross for a
careful reading of the manuscript, and to P.G. Kwiat,
A. Steinberg, and Professor R.Y. Chiao for valuable dis-
cussions about the content of the paper. This work was
supported by the Director, OKce of Energy Research,
Office of High Energy and Nuclear Physics, Division o
High Energy Physics of the U.S. Department of Energy
under Contract No. DE-AC03-76SF00098.
[1] A. Einstein et al., Phys. Rev. 47, 777 (1935).
[2] J.S. Bell, Physics 1, 195 (1964).
[3] J.F. Clauser et al. , Phys. Rev. Lett. 23, 880 (1969).
[4] B.S. Cirel'son, Lett. Math. Phys. 4, 93 (1980).
[5] N. Gisin and A. Peres, Phys. Lett. 65, 1838 (1990).
[6] S.L. Braunstein et aL, Phys. Rev. Lett. 68, 3259 (1992).
[8] N.D. Mermin, ¹tuTechniques and and Ideas in Quan
turn Measurement Theory, edited by D.M. Greenberger
(New York Academy of Science, New York, 1986)
pp. 422—428.
[9] P.H. Eberhard, Nuovo Cim. SSB, 75 (1977).
[10] P.H. Eberhard, Nuovo Cim. 46B, 392 (1978).
10
2
1
0.5
ca 0.2
CO
0.01
0.05—
~ 0
IQ
o~
0.02—
I I i I I I
65 70 75 80 85 90 95 100
Efficiency q (%)
FIG. 1. Maximum a8'ordable background vs efBciency: ~,
optimized conditions; o, conditions of Eqs. (1)—(5).
pi =M/2
respectively, and using the values of r, u, and o.q
—o.2
(—:Pi —P2) given in Table II. Note that, for rl = 1, the
vector Qo reduces to the value given by Eq. (1), and the
angles ni, n2, Pi, and Pq reduce to the values given by
Eqs. (2)—(5).
1
2/1+ rz
(31)
g.
o angles ni —n2 and Pi —P2 could always be
o be the same, or the opposite of one another, as
understood from an analytic study of Eqs. (10)
7). The vector @ turned out to be of the form
Eqs. (2)—(5).
In conclusion, it is possible to perform a loophole-free
experiment if the eKciency g of the photon counters is
higher than 66.7' and the background is less than the
value indicated on Fig. 1 for that value of g. For small
background levels, it is possible to perform a loophole-
free EPR experiment with a less than 82.8% counter ef-
B.ciency.
an be reached in the two-photon experiment con-
in this paper by first superposing states I
~I &
~& in unequal amounts,
(32)
= (~/2) —90', (33)
tating the planes of polarization of a and of b in
ni, Pi) by the angles
ACKNO%'LEDG MENTS
The author is indebted to Professor R.R. Ross for a
careful reading of the manuscript, and to P.G. Kwiat,
A. Steinberg, and Professor R.Y. Chiao for valuable dis-
cussions about the content of the paper. This work was
supported by the Director, OKce of Energy Research,
Office of High Energy and Nuclear Physics, Division of
High Energy Physics of the U.S. Department of Energy
under Contract No. DE-AC03-76SF00098.
Einstein et al., Phys. Rev. 47, 777 (1935).
. Bell, Physics 1, 195 (1964).
. Clauser et al. , Phys. Rev. Lett. 23, 880 (1969).
S. Cirel'son, Lett. Math. Phys. 4, 93 (1980).
Gisin and A. Peres, Phys. Lett. 65, 1838 (1990).
[8] N.D. Mermin, ¹tuTechniques and and Ideas in Quan
turn Measurement Theory, edited by D.M. Greenberger
(New York Academy of Science, New York, 1986),
pp. 422—428.
[9] P.H. Eberhard, Nuovo Cim. SSB, 75 (1977).
P.H. Eberhard (1993)

Theoretical no-signalling probabilities, × 4 // Observed relative frequencies, × 10^6
Bob Setting 1 Bob Setting 2
Outcomes “ d ” “ n “ “ d ” “ n “
Alice Setting 1
“ d ” 1 + a1 + b1 + z11 1 + a1 – b1 – z11 2 + 2 a1 1 + a1 + b2 + z12 1 + a1 – b2 – z12 2 + 2 a1
“ n “ 1 – a1 + b1 – z11 1 – a1 – b1 + z11 2 – 2 a1 1 – a1 + b2 – z12 1 – a1 – b2 + z12 2 – 2 a1
2 + 2 b1 2 – 2 b1 4 2 + 2 b2 2 – 2 b2 4
Alice Setting 2
“ d ” 1 + a2 + b1 + z21 1 + a2 – b1 – z21 2 + 2 a2 1 + a2 + b2 + z22 1 + a2 – b2 – z22 2 + 2 a2
“ n “ 1 – a2 + b1 – z21 1 – a2 – b1 + z21 2 – 2 a2 1 – a2 + b2 – z22 1 – a2 – b2 + z22 2 – 2 a2
2 + 2 b1 2 – 2 b1 4 2 + 2 b2 2 – 2 b2 4
162 84 168 78
87 999668 373 999381
10 ^ 6 *
VIENNA
181 485 10 658
67 999267 530 998802
J = 27 S = CHSH = 2,000108
4 J = (1 + a1 + b1 + z11)
– (1 – a2 + b1 – z21)
– (1 + a1 – b2 – z12)
– (1 + a2 + b2 + z22)
= – 2 + (z11 + z21 + z12 – z22)
4 rho 11
= (2 + 2 z11) – (2 – 2 z11)
= 4 z11
4 S = 4 CHSH
= 4 (z11 + z12 + z21 – z22)
S = z11 + z12 + z21 – z22
= 2 + 4 J
J = (S - 2) / 4
VIENNA

4 rho 11 = (2 + 2 z11) – (2 – 2 z11) = 4 z11
4 S = 4 CHSH = 4 (z11 + z12 + z21 – z22)
4 J = (1 + a1 + b1 + z11)
– (1 – a2 + b1 – z21)
– (1 + a1 – b2 – z12)
– (1 + a2 + b2 + z22)
= – 2 + (z11 + z21 + z12 – z22)
S = z11 + z12 + z21 – z22 = 2 + 4 J
J = (S - 2) / 4
Estimation, standard errors, p-values
Routine MLE (Sir R.A. Fisher 1921…)
Log Lik = N(dd|11)log(1 + a1 +b1 +z11) +
… [15 more terms]
Parameters: a1 a2 b1 b2 z11 z12 z21 z22
Get mle of z11 + z21 + z12 – z22
Get estimated standard error of z11 + z21 + z12 – z22
from Fisher information matrix
Asymptotically optimal
[Linear constraints?]
Modern approach:
algebraic geometry, computer algebra
Poor man’s solution:
two stage, generalised, least squares
Asymptotically just as good as MLE!
Also possible: amusing hybrid solutions
*Also* asymptotically optimal

A standard Bell-type experiment with
I two parties,
I two measurement settings per party,
I two possible outcomes per measurement setting per party,
generates a vector of 16 = 4 ⇥ 4 numbers of outcome combinations per setting
combination.
This applies both to the CHSH case (assuming there are no “non detections”) and to the
Eberhard case (after merging two each of three possible outcomes per measurement).
The four sets of four counts can be thought of as four observations each of a
multinomially distributed vector over four categories.
Next ≈10 slides:
Work in progress: the theory

Write Xij for the number of times outcome combination j was observed, when setting
combination i was in force.
Let ni be the total number of trials with the ith setting combination.
The four random vectors ~Xi = (Xi1, Xi2, Xi3, Xi4), i = 1, 2, 3, 4,
are independent each with a Multinomial(ni ; ~pi ) distribution,
where ~pi = (pi1, pi2, pi3, pi4).

The 16 probabilities pij are estimated by relative frequencies bpij = Xij /ni and have the
following variances and covariances:
var(bpij ) = pij (1 pij )/ni ,
cov(bpij , bpij0 ) = pij pij0 /ni for j 6= j0
,
cov(bpij , bpi0j0 ) = 0 for i 6= i0
.
The variances and covariances can be arranged in a
16 ⇥ 16 block diagonal matrix ⌃ of four 4 ⇥ 4 diagonal blocks of non-zero elements.
Arrange the 16 estimated probabilities and their true values correspondingly in (column)
vectors of length 16.
I will denote these simply by bp and p respectively.
We have E(bp) = p 2 R16 and cov(bp) = ⌃ 2 R16⇥16.

We are interested in the value of one particular linear combination of the pij , let us
denote it by ✓ = a>p.
We know that four other particular linear combinations are identically equal to zero: the
so-called no-signalling conditions.
This can be expressed as B>p = 0 where the 16 ⇥ 4 matrix B contains, as its four
columns, the coeﬃcients of the four linear combinations.
We can sensibly estimate ✓ by b✓ = a> bp c>B> bp where c is any vector of dimension 4.
For whatever choice we make, Ebp = p.
We propose to choose c so as to minimise the variance of the estimator. This
minimization problem is a well-known problem from statistics and linear algebra (“least
squares”).
𝜃 𝜃

Deﬁne
var(a>
bp) = a>
⌃a = ⌃aa,
cov(a>
bp, B>
bp) = a>
⌃B = ⌃aB,
var(B>
bp) = B>
⌃B = ⌃BB;
then the optimal choice for c is
copt = ⌃aB⌃ 1
BB
leading to the optimal variance
⌃aa ⌃aB⌃ 1
BB⌃Ba.
:
:
:

In the experimental situation we do not know p in advance, hence also do not know ⌃
in advance. However we can estimate it in the obvious way (“plug-in”) and for ni ! 1
we will have, just as in the previous section, an asymptotic normal distribution for our
“approximately best” Bell inequality estimate, with an asymptotic variance which can be
estimated by natural “plug-in” procedure, leading again to asymptotic conﬁdence
intervals, estimated standard errors, and so on.
The asymptotic width of these conﬁdence intervals are the smallest possible and
correspondingly the number of standard errors deviation from “local realism” the largest
possible.
The fact that c is not known in advance does not harm these results.
“two stage (generalised) least squares”

table11 <- matrix(c(141439, 73391, 76224, 875392736),  
2, 2, byrow = TRUE, 
dimnames = list(Alice = c("d", "n"), Bob = c("d", "n"))) 
table12 <- matrix(c(146831, 67941, 326768, 874976534),  
dimnames = list(Alice = c("d", "n"), Bob = c("d", "n"))) 
table21 <- matrix(c(158338, 425067, 58742, 875239860),  
dimnames = list(Alice = c("d", "n"), Bob = c("d", "n")))  
table22 <- matrix(c(8392, 576445, 463985, 874651457),  
dimnames = list(X = c("d", "n"), Y = c("d", “n")))
Next ≈10 slides:
Work in progress: the practice

table11
## Bob 
## Alice d n 
## d 141439 73391 
## n 76224 875392736
table12
## Bob 
## Alice d n 
## d 146831 67941 
## n 326768 874976534
table21
## Bob 
## Alice d n 
## d 158338 425067 
## n 58742 875239860
table22

## Y 
## X d n 
## d 8392 576445 
## n 463985 874651457
tables <- cbind(as.vector(t(table11)), as.vector(t(table12)),  
as.vector(t(table21)), as.vector(t(table22))) 
tables
## [,1] [,2] [,3] [,4] 
## [1,] 141439 146831 158338 8392 
## [2,] 73391 67941 425067 576445 
## [3,] 76224 326768 58742 463985 
## [4,] 875392736 874976534 875239860 874651457
dimnames(tables) = list(outcomes = c("dd", "dn", "nd", "nn"),  
settings = c(11, 12, 21, 22))

tables
## settings 
## outcomes 11 12 21 22 
## dd 141439 146831 158338 8392 
## dn 73391 67941 425067 576445 
## nd 76224 326768 58742 463985 
## nn 875392736 874976534 875239860 874651457
Ns <- apply(tables, 2, sum) 
Ns
## 11 12 21 22  
## 875683790 875518074 875882007 875700279
rawProbsMat <- tables / outer(rep(1,4), Ns) 
rawProbsMat
## settings 
## outcomes 11 12 21 22 
## dd 1.615183e-04 1.677076e-04 1.807755e-04 9.583188e-06 
## dn 8.380993e-05 7.760091e-05 4.853017e-04 6.582675e-04 
## nd 8.704512e-05 3.732282e-04 6.706611e-05 5.298445e-04 
## nn 9.996676e-01 9.993815e-01 9.992669e-01 9.988023e-01

VecNames <- as.vector(t(outer(colnames(rawProbsMat),  
rownames(rawProbsMat), paste, sep = ""))) 
VecNames
## [1] "11dd" "11dn" "11nd" "11nn" "12dd" "12dn" "12nd" "12nn" "21dd" "21dn" 
## [11] "21nd" "21nn" "22dd" "22dn" "22nd" "22nn"
rawProbsVec <- as.vector(rawProbsMat) 
names(rawProbsVec) <- VecNames 
VecNames
## [1] "11dd" "11dn" "11nd" "11nn" "12dd" "12dn" "12nd" "12nn" "21dd" "21dn" 
## [11] "21nd" "21nn" "22dd" "22dn" "22nd" “22nn"
rawProbsVec
## 11dd 11dn 11nd 11nn 12dd  
## 1.615183e-04 8.380993e-05 8.704512e-05 9.996676e-01 1.677076e-04  
## 12dn 12nd 12nn 21dd 21dn  
## 7.760091e-05 3.732282e-04 9.993815e-01 1.807755e-04 4.853017e-04  
## 21nd 21nn 22dd 22dn 22nd  
## 6.706611e-05 9.992669e-01 9.583188e-06 6.582675e-04 5.298445e-04  
## 22nn  
## 9.988023e-01

Aplus <- c(1, 1, 0, 0) 
Aminus <- - Aplus 
Bplus <- c(1, 0, 1, 0) 
Bminus <- - Bplus 
zero <- c(0, 0, 0, 0) 
NSa1 <- c(Aplus, Aminus, zero, zero) 
NSa2 <- c(zero, zero, Aplus, Aminus) 
NSb1 <- c(Bplus, zero, Bminus, zero) 
NSb2 <- c(zero, Bplus, zero, Bminus) 
NS <- cbind(NSa1 = NSa1, NSa2 = NSa2, NSb1 = NSb1, NSb2 = NSb2) 
rownames(NS) <- VecNames

NS
## NSa1 NSa2 NSb1 NSb2 
## 11dd 1 0 1 0 
## 11dn 1 0 0 0 
## 11nd 0 0 1 0 
## 11nn 0 0 0 0 
## 12dd -1 0 0 1 
## 12dn -1 0 0 0 
## 12nd 0 0 0 1 
## 12nn 0 0 0 0 
## 21dd 0 1 -1 0 
## 21dn 0 1 0 0 
## 21nd 0 0 -1 0 
## 21nn 0 0 0 0 
## 22dd 0 -1 0 -1 
## 22dn 0 -1 0 0 
## 22nd 0 0 0 -1 
## 22nn 0 0 0 0

cov11 <- diag(rawProbsMat[ , "11"]) - outer(rawProbsMat[ , "11"], rawProbsMat[ , "11"]) 
Cov <- matrix(0, 16, 16) 
rownames(Cov) <- VecNames 
colnames(Cov) <- VecNames 
Cov[1:4, 1:4] <- cov11/Ns["11"] 
Cov[5:8, 5:8] <- cov12/Ns["12"] 
Cov[9:12, 9:12] <- cov21/Ns["21"] 
Cov[13:16, 13:16] <- cov22/Ns["22"] 
 
J <- c(c(1, 0, 0 ,0), - c(0, 1, 0 ,0), - c(0, 0, 1, 0), - c(1, 0, 0, 0)) 
names(J) <- VecNames 
sum(J * rawProbsVec)
## [1] 7.26814e-06
varJ <- t(J) %*% Cov %*% J 
covNN <- t(NS) %*% Cov %*% NS 
covJN <- t(J) %*% Cov %*% NS 
covNJ <- t(covJN)

## Estimated variance of optimal test based on J 
varJ - covJN %*% solve(covNN) %*% covNJ
## [,1] 
## [1,] 1.594636e-13
## Estimated variance of Eberhard's J 
varJ
## [,1] 
## [1,] 3.605539e-13
sqrt(varJ / (varJ - covJN %*% solve(covNN) %*% covNJ))
## [,1] 
## [1,] 1.503676
covJN %*% solve(covNN)
## NSa1 NSa2 NSb1 NSb2 
## [1,] 0.395483 0.05436871 0.3516065 0.06982674
Jopt <- J - covJN %*% solve(covNN) %*% t(NS)

Jopt
## 11dd 11dn 11nd 11nn 12dd 12dn 12nd 
## [1,] 0.2529105 -0.395483 -0.3516065 0 0.3256562 -0.604517 -0.06982674 
## 12nn 21dd 21dn 21nd 21nn 22dd 22dn 
## [1,] 0 0.2972378 -0.05436871 -0.6483935 0 -0.8758045 0.05436871 
## 22nd 22nn 
## [1,] 0.06982674 0

sum(J * rawProbsVec)
## [1] 7.26814e-06
sum(Jopt * rawProbsVec)
## [1] 6.997615e-06
varJ / (varJ - covJN %*% solve(covNN) %*% covNJ)
## [,1] 
## [1,] 2.261042
(varJ - covJN %*% solve(covNN) %*% covNJ) / varJ
## [,1] 
## [1,] 0.442274
sqrt( (varJ - covJN %*% solve(covNN) %*% covNJ) / varJ )
## [,1] 
## [1,] 0.6650368

Part 2
Discussion: ¿ QIR - IF ?

⸘Quantum Buddhism‽
⸘…‽

The Goals of Science, according to QBism
1. To guide action.
2. To learn about the character of the world.
R¨udiger Schack Royal Holloway, University of London Why QBism is immune to no-go theorems
The B in QBism
Bayesian? NO
Bruno de Finetti? Better
B? Current default position
Bettabilitarian?
R¨udiger Schack Royal Holloway, University of London Why QBism is immune to no-go theorems
My answer:
The “B” in QBism is …
the “B” of the Buddha!
Rudiger Schack
Slides of Rudiger’s Växjö talk

Erwin Schrödinger
• I don't like it, and I'm sorry I ever had anything to do with it.
[About the probability interpretation of quantum mechanics.] Epigraph, without citation, in John Gribbin, In
Search of Schrödinger’s Cat: Quantum Physics and Reality (1984), v, frontispiece.

• If all this damned quantum jumping were really here to stay, I should be sorry, I should be sorry I ever got
involved with quantum theory.
As reported by Heisenberg describing Schrödinger’s time spent debating with Bohr in Copenhagen (Sep 1926). In Werner
Heisenberg, Physics and Beyond: Encounters and Conversations (1971), 75. As cited in John Gribbin, Erwin Schrodinger and the
Quantum Revolution.

• God knows I am no friend of probability theory, I have hated it from the ﬁrst moment when our dear
friend Max Born gave it birth. For it could be seen how easy and simple it made everything, in principle,
everything ironed and the true problems concealed. Everybody must jump on the bandwagon [Ausweg]. And
actually not a year passed before it became an oﬃcial credo, and it still is.
Letter to Albert Einstein (13 June 1946), as quoted by Walter Moore in Schrödinger: Life and Thought (1989) ISBN 0521437679

The experiments of 2015 convinced me …
rebrand “spooky action at a distance” …
• Entanglement is an asset, not a horror

• We call it “spooky” because our mammal brains, trained by evolution, can’t
“understand” it any way except as the work of a *potentially* malevolent “agent”

• “Spooky” is an inadequate translation of “spukhaft”. We have to say it in German.

• “Passion at a distance” is better

• More precise “(Martingale like) disciplined passion at a distance”? No, it won’t catch on …

• Auserlesene / engelhafte ‘spukhafte Fernwirkung’ (exquisite / angelic “action at a distance”)

… and …
Belavkin’s “eventum mechanics” is the way to go.
• It’s a “collapse theory”

• It is therefore “non-local”

• It can be made Lorentz invariant!

• Some famous recent works conﬁrm me in my opinions:

• Daniela Frauchiger & Renato Renner

[My title] Schrödinger’s cat, the Wigners, and the Wigners’ friend

• Gilles Brassard & Paul Raymond-Robichaud

“The equivalence of local-realistic and no-signalling theories”. Abstract: We provide a framework to
describe all local-realistic theories and all no-signalling operational theories. We show that when the
dynamics is reversible, these two concepts are equivalent. In particular, this implies that unitary
quantum theory can be given a local-realistic model.

Eugene Paul Wigner
Amelia Zippora Wigner-Frank Leo Szilard
>
>
>
>
The Wigners’ friend
Quantum system / cat in a box / …

My prejudice:
The clicks are “real”, the rest … a
construction of our minds
• It is allowed to imagine that more stuﬀ is real

• Such a “dilation” need not be unique

• “QM without collapse”, or Unitary QM - several theories, best known being MW
and Quantum Qubism

• MW is many words

• QB is subjective Bayes … but I’m a frequentist … usually Bayes and frequentist
inference agree … it’s really interesting when they disagree !!!

• Quantum Buddhism gives yet further insights

F&R: The Wigners’ friend
• QM *without collapse* + MW implies only the wave
function is real

• QM *without collapse* + Qbism implies nothing is real

• My conclusion: QM without collapse is non-sense!

B&RR
• They insist on irreversibility!

• Change deﬁnitions of everything

• It’s brilliant but … it’s very technical and very long

• My conclusion: we must trash *irreversibility*

Conclusion: QIR - IF
• “Spukhafte fernwerkung” is for real and … Exquisite? Angelic?

• Collapse is real

• Recommendation: take a look again at Belavkin’s “Eventum Mechanics”

• Congratulations and deep thanks to Andrei for *yet another* splendid conference,
the pinnacle of twenty years of splendid conferences

• Quantum Information Revolution Impacted Foundations at Växjö (2019)

• We must keep questioning the very words which we use (Eastern thought / Western
post-modernism) … and remember what we are … *nothing* is real - QBism!

Postjudice:
Everything is a construction of our minds - there is nothing else
Beware: every word is a “model”
All models are wrong, some are useful
Combray

A toast to Andrei Khrennikov
“Zeer oude genever”
The juniper-ﬂavoured national and
traditional liquor of the Netherlands and Belgium,
from which gin evolved.
There is a tradition that attributes the
invention of jenever to the Leiden
chemist and alchemist Sylvius
(Franciscus Sylvius de Bouve)

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