Asymmetric multipartite GHZ states and Bell inequalities
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This document outlines the talk of Darwin Gosal on asymmetric multipartite GHZ states and Bell inequalities. The talk covers generalized GHZ states, Gisin's theorem on two-particle states violating Bell inequalities, different Bell inequalities including CHSH and Werner-Wolf-Zukowski-Brukner correlation functions, a numerical method for testing classical descriptions, and results showing GHZ states violate Bell inequalities for odd numbers of qubits.
Asymmetric multipartite GHZ states and Bell inequalities
- 1. Asymmetric multipartite GHZ states and Bell inequalities Darwin Gosal phydg@nus.edu.sg National University of Singapore
- 2. Talk Outline Generalized GHZ states
- 3. Talk Outline Generalized GHZ states Gisin’s theorem
- 4. Talk Outline Generalized GHZ states Gisin’s theorem Bell inequalities
- 5. Talk Outline Generalized GHZ states Gisin’s theorem Bell inequalities Numerical method
- 6. Talk Outline Generalized GHZ states Gisin’s theorem Bell inequalities Numerical method Discussion and conclusions
- 7. Generalized GHZ states 1 1 |ψ = √ |000 + √ |111 2 2
- 8. Generalized GHZ states 1 1 |ψ = √ |000 + √ |111 2 2 |ψ = cos α|0, . . . , 0 + sin α|1, . . . , 1
- 9. Gisin’s Theorem Any pure non-product state of two particles violates the CHSH inequalities. Physics Letters A 162, 15 (1992)
- 10. Gisin’s Theorem Any pure non-product state of two particles violates the CHSH inequalities. Physics Letters A 162, 15 (1992) Can Gisin’s theorem be generalized to N-qubit states?
- 11. Bell inequalities Clauser-Horne-Shimony-Holt inequality
- 12. Bell inequalities Clauser-Horne-Shimony-Holt inequality Clauser-Horne inequality
- 13. Bell inequalities Clauser-Horne-Shimony-Holt inequality Clauser-Horne inequality Werner-Wolf-Zukowski-Brukner correlation-function
- 14. WZB correlation-functions 1 ρ = 3 (1 + a · λ ⊗ I ⊗ I + I ⊗ b · λ ⊗ I + I ⊗ I ⊗ c · λ N (AB) (AC) + Tkl λk ⊗ λl ⊗ I + Tkl λk ⊗ I ⊗ λl k,l k,l (BC) (ABC) + Tkl I ⊗ λ k ⊗ λl + k,l,m Tklm λk ⊗ λ l ⊗ λ m k,l
- 15. WZB correlation-functions 1 ρ = 3 (1 + a · λ ⊗ I ⊗ I + I ⊗ b · λ ⊗ I + I ⊗ I ⊗ c · λ N (AB) (AC) + Tkl λk ⊗ λl ⊗ I + Tkl λk ⊗ I ⊗ λl k,l k,l (BC) (ABC) + Tkl I ⊗ λ k ⊗ λl + k,l,m Tklm λk ⊗ λ l ⊗ λ m k,l
- 16. WZB correlation-functions sin 2α ≤ 2(1−N )/2 for odd N
- 17. WZB correlation-functions sin 2α ≤ 2(1−N )/2 for odd N √ F < 1 − 1/(sin(2α) 2N −1 )
- 18. 2-particle correlations based on CHSH All multi-particle entangled states violates local realism provided post-selections are allowed Popescu and Rohrlich PLA 166, 293 (1992)
- 19. 2-particle correlations based on CHSH All multi-particle entangled states violates local realism provided post-selections are allowed Popescu and Rohrlich PLA 166, 293 (1992) 1 Fthr =1− √ 1 + sin2 (2α)( 2N −1−k − 1)
- 20. Numerical method Using linear optimization method, we have necessary and sufficient conditions for the existance of a classical description of the given correlations. ρ = (1 − F )|ψ ψ| + F ρnoise
- 21. Numerical method Using linear optimization method, we have necessary and sufficient conditions for the existance of a classical description of the given correlations. ρ = (1 − F )|ψ ψ| + F ρnoise 1 where the white noise is 2N I
- 22. Numerical method Using linear optimization method, we have necessary and sufficient conditions for the existance of a classical description of the given correlations. ρ = (1 − F )|ψ ψ| + F ρnoise 1 where the white noise is 2N I PRL 85, 4418; PRA 66, 032103
- 23. Result (3-qubit GHZ state) 0.5 0.5 Numerical WWZB CHSH 0.4 0.4 0.3 0.3 F 0.2 0.2 0.1 0.1 0 0 0 0 π/16 6 π/8 12 3π/16 18 π/4 24 α
- 24. Conclusions WWZB inequalities cannot detect (N − k)-particle correlations
- 25. Conclusions WWZB inequalities cannot detect (N − k)-particle correlations CHSH inequalities is not equivalent with CH inequality for three qubits
- 26. Conclusions WWZB inequalities cannot detect (N − k)-particle correlations CHSH inequalities is not equivalent with CH inequality for three qubits Gisin’s theorem hold for odd number of qubit in the GHZ states
- 27. Questions ???