aqora

Quantum Contextuality in a Nutshell

Zhenghao Liu

Springer thesesJan 1, 20230 citations

A Logical Formalism of Hardy-type Paradox

Songyi Liu, Yongjun Wang, Baoshan Wang +2 more

Hardy-type paradoxes provide elegant, inequality-free proofs of quantum contextuality. We introduce a unified logical formalism for these paradoxes, termed logical Hardy-type paradoxes. For any finite quantum scenario of ideal measurements, we prove that the existence of a logical Hardy-type paradox is equivalent to logical contextuality. Specifically, strong contextuality is equivalent to logical Hardy-type paradoxes with success probability SP = 1. These results generalize prior work on (2,k,2), (2,2,d), and n-cycle scenarios. We analyze logical Hardy-type paradoxes in the Mansfield and Klyachko-Can-Binicioglu-Shumovsky (KCBS) scenarios. In the KCBS scenario, we show that there is exactly one type of logical Hardy-type paradox, achieving SP\approx 10.56% for a specific parameter setting.Hardy-type paradoxes provide elegant, inequality-free proofs of quantum contextuality. We introduce a unified logical formalism for these paradoxes, termed logical Hardy-type paradoxes. For any finite quantum scenario of ideal measurements, we prove that the existence of a logical Hardy-type paradox is equivalent to logical contextuality. Specifically, strong contextuality is equivalent to logical Hardy-type paradoxes with success probability SP = 1. These results generalize prior work on (2,k,2), (2,2,d), and n-cycle scenarios. We analyze logical Hardy-type paradoxes in the Mansfield and Klyachko-Can-Binicioglu-Shumovsky (KCBS) scenarios. In the KCBS scenario, we show that there is exactly one type of logical Hardy-type paradox, achieving SP\approx 10.56% for a specific parameter setting.

quant-pharXiv:2601.01445Jan 6, 20260 citations

Twin inequality for fully contextual quantum correlations

Adán Cabello

Quantum mechanics exhibits a very peculiar form of contextuality. Identifying and connecting the simplest scenarios in which more general theories can or cannot be more contextual than quantum mechanics is a fundamental step in the quest for the principle that singles out quantum contextuality. The former scenario corresponds to the Klyachko-Can-Binicio\ifmmode \breve{g}\else \u{g}\fi{}lu-Shumovsky (KCBS) inequality. Here we show that there is a simple tight inequality, twin to the KCBS, for which quantum contextuality cannot be outperformed. In a sense, this twin inequality is the simplest tool for recognizing fully contextual quantum correlations.Quantum mechanics exhibits a very peculiar form of contextuality. Identifying and connecting the simplest scenarios in which more general theories can or cannot be more contextual than quantum mechanics is a fundamental step in the quest for the principle that singles out quantum contextuality. The former scenario corresponds to the Klyachko-Can-Binicio\ifmmode \breve{g}\else \u{g}\fi{}lu-Shumovsky (KCBS) inequality. Here we show that there is a simple tight inequality, twin to the KCBS, for which quantum contextuality cannot be outperformed. In a sense, this twin inequality is the simplest tool for recognizing fully contextual quantum correlations.

arXiv:1209.0112Physical Review AJan 30, 201319 citations

Contextual Approach to Quantum Theory

Andrei Yu. Khrennikov

Springer eBooksJan 1, 20043 citations

Analysis of Some Recent Tests of Quantum Contextuality

Brian R. La Cour, Andrei Yu. Khrennikov

AIP conference proceedingsJan 1, 20100 citations

Effect of decoherence on the contextual and nonlocal properties of a biphoton

Assaf Shaham, H. S. Eisenberg

Quantum contextuality is a nonintuitive property of quantum mechanics that distinguishes it from any classical theory. A complementary quantum property is quantum nonlocality, which is an essential resource for many quantum information tasks. Here we experimentally study the contextual and nonlocal properties of polarization biphotons. First, we investigate the ability of the biphotons to exhibit contextuality by testing the violation of the Klyachko-Can-Binicio\ifmmode \breve{g}\else \u{g}\fi{}lu-Shumovsky (KCBS) inequality. In order to do so, we used the original protocol suggested in the KCBS paper and adjusted it to the real scenario, where some of the biphotons are distinguishable. Second, we transmitted the biphotons through different unital channels with a controlled amount of noise. We measured the decohered output states and demonstrated that the ability to exhibit quantum contextuality using the KCBS inequality is more fragile to noise than the ability to exhibit nonlocality.Quantum contextuality is a nonintuitive property of quantum mechanics that distinguishes it from any classical theory. A complementary quantum property is quantum nonlocality, which is an essential resource for many quantum information tasks. Here we experimentally study the contextual and nonlocal properties of polarization biphotons. First, we investigate the ability of the biphotons to exhibit contextuality by testing the violation of the Klyachko-Can-Binicio\ifmmode \breve{g}\else \u{g}\fi{}lu-Shumovsky (KCBS) inequality. In order to do so, we used the original protocol suggested in the KCBS paper and adjusted it to the real scenario, where some of the biphotons are distinguishable. Second, we transmitted the biphotons through different unital channels with a controlled amount of noise. We measured the decohered output states and demonstrated that the ability to exhibit quantum contextuality using the KCBS inequality is more fragile to noise than the ability to exhibit nonlocality.

arXiv:1410.3640Physical Review AFeb 27, 20154 citations

The Degree of Quantum Contextuality in Terms of Concurrence for the KCBS Scenario

Related papers

The Degree of Quantum Contextuality in Terms of Concurrence for the KCBS Scenario

Related papers