Quantum violation of I_{3322} inequality

Abstract

Abstract: Quantum non-locality is a necessary resource for quantum information processing. Recently, I3322 inequality, used as a powerful tool for judging non-locality, has attracted much attention. Considering the non-ideal factors in judging non-locality, MATLAB is used to simulate the quantum violation of inequality influenced by an entanglement state, mixed entanglement states, and noise channels. Results show that for an entanglement state, quantum violation is found when the degree of entanglement is larger than a threshold value. For mixed entanglement states, quantum violation is found in larger parameter regions. Under two-Kraus-operator channels, phase diagram relating to quantum violation is found in the noise parameter space. The results are useful to quantum information processing based on I3322 inequality.

Key words: quantum information, non-locality, Bell-like inequality, maximum quantum violation; quantum noise channel

CLC Number:

O431.2

GUO Mengqi, GONG Longyan∗. Quantum violation of I_{3322} inequality[J]. Chinese Journal of Quantum Electronics, 2021, 38(1): 50-56.

References 26

[1]	Barrett J, Colbeck R, Kent A. Memory attacks on device-independent quantum cryptography [J]. Physical Review Letters,
20	13, 110(1): 010503.
[2]	Prevedel T, Walther P, Tiefenbacher F. High-speed linear optics quantum computing using active feed-forward [J]. Nature,
20	07, 445(5346): 65-69.
[3]	Cavalcanti D, Ac´ın A, Brunner N, et al. All quantum states useful for teleportation are nonlocal resources [J]. Physical Review
	A, 2013, 87(4): 042104.
[4]	Pironio S, Acin A, Massar S, et al. Random numbers certified by Bell’s theorem [J]. Nature, 2010, 464(7291): 1021-1024.
[5]	Bell J. On the Einstein-Podolsky-Rosen paradox [J]. Physics, 1964, 1(3): 195-200.
[6]	Clauser J, Horne M, Shimony A, et al. Proposed experiment to test local hidden-variable theories [J]. Physical Review Letters,
19	69, 23(15): 880-884.
[7]	Fine A. Hidden variables, joint probability, and the Bell inequalities [J]. Physical Review Letters, 1982, 48(5): 291-295.
[8]	Clauser J, Horne M. Experimental consequences of objective local theories [J]. Physical Review D, 1974, 10(2): 526-535.
[9]	Garg A, Mermin N. Correlation inequalities and hidden variables [J]. Physical Review Letters, 1982, 49(17): 1220-1223.
[10]	Pitowsky I, Svozil K. New optimal tests of quantum nonlocality [J]. Physical Review A, 2001, 64(1): 014102.
[11]	Brunner N, Gisin N. Partial list of bipartite Bell inequalities with four binary settings [J]. Physics Letters A, 2008, 372(18):
31	62-3167.
[12]	Cruzeiro E, Gisin N. Complete list of tight Bell inequalities for two parties with four binary settings [J]. Physical Review A,
20	19, 99(2): 022104.
[13]	Collins D, Gisin N. A relevant two qubit Bell inequality inequivalent to the CHSH inequality [J]. Journal of Physics A, 2004,
37	(5): 1775-1787.
[14]	Pal K, V´ertesi T. Quantum bounds on Bell inequalities [J]. Physical Review A, 2009, 79(2): 022120.
[15]	Navascues N, Pironio S, Ac´ın A. A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
[J]	New Journal of Physics, 2008, 10(7): 073013.
[16]	Zhao J Q, Cao L Z, Wang X Q, et al. Experimental investigation of different Bell-type inequality in three-qubit Greenberger-
	Horne-Zeilinger states [J]. Acta Physica Sinica, 2012, 61(17): 170301.
	赵加强, 曹连振, 王晓芹, 等. 三光子GHZ 态中不同Bell 型不等式的实验研究[J]. 物理学报, 2012, 61(17): 170301.
[17]	Zhao J Q, Cao L Z, Lu H X, et al. Bell-type inequality and tripartite nonlocality in three-qubit GHZ-class states [J]. Acta
	Physica Sinica, 2013, 62(12): 120301.
	赵加强, 曹连振, 逯怀新, 等. 三比特类GHZ 态的Bell 型不等式和非定域性[J]. 物理学报, 2013, 62(12): 120301.
[18]	Ekert A. Quantum cryptography based on Bell’s theorem [J]. Physical Review Letters, 1991, 67(6): 661-663.
[19]	Zhao J Q, Cao L Z, Yang Y, et al. Nonlocality and robustness in two-photon entangled system [J]. Chinese Journal of Quantum
	Electronics, 2018, 35(4): 451-454.
	赵加强, 曹连振, 杨阳等. 双光子纠缠体系中的非定域性和稳健性[J]. 量子电子学报, 2018, 35(4): 451-454.
[20]	Yao J X, Gong L Y. Influence of quantum entanglement and quantum operation on superiority of CHSH quantum game [J].
	Chinese Journal of Quantum Electronics, 2015, 32(5): 581-585.
	姚嘉祥, 巩龙延. 量子纠缠和量子操作对CHSH 量子博弈优越性的影响[J]. 量子电子学报, 2015, 32(5): 581-585.
[21]	Su X Q, Guo G C. Quantum communication and quantum computation [J]. Chinese Journal of Quantum Electronics, 2014,
21	(6): 706-718.
	苏晓琴, 郭光灿. 量子通信与量子计算[J]. 量子电子学报, 2004, 21(6): 706-718.
[22]	Laskowski W, Paterek T, Zukowski M, et al. Tight multipartite Bell’s inequalities involving many measurement settings [J].
	Physical Review Letters, 2004, 93(20): 200401.
[23]	Son W, Lee J, Kim M. Generic Bell inequalities for multipartite arbitrary dimensional systems [J]. Physical Review Letters,
20	06, 96(6): 060406.
[24]	Ac´ın A, Gill R, Gisin N. Optimal Bell tests do not require maximally entangled states [J]. Physical Review Letters, 2005,
95	(21): 210402.
[25]	Froissart M. Constructive generalization of Bell’s inequalities [J]. IL Nuovo Cimento B, 1981, 64(2): 241-251.
[26]	Ruan L, Dai W, Win M. Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels [J]. Physical
	Review A, 2018, 97(5): 052332.