Bell’s Nonlocality in a General Nonsignaling Case: Quantitatively and Conceptually

Loubenets, Elena R.

doi:10.1007/s10701-017-0077-4

Cited by 19 publications

(39 citation statements)

References 41 publications

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“…with arbitrarily chosen positive integers γ m , then, under representation (15), to an observable (41) there also corresponds the unit vector r X ′ ∈ R (0) d , for which the projection r (−) X ′ = 0, so that r X ′ = r (+)…”

Section: Two-qudit States With Perfect Correlations/anticorrelationsmentioning

confidence: 99%

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Quantum analog of the original Bell inequality for two-qudit states with perfect correlations/anticorrelations

Loubenets

Khrennikov

2019

J. Phys. A: Math. Theor.

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For an even qudit dimension d ≥ 2, we introduce a class of two-qudit states exhibiting perfect correlations/anticorrelations and prove via the generalized Gell-Mann representation that, for each two-qudit state from this class, the maximal violation of the original Bell inequality is bounded from above by the value 3/2 -the upper bound attained on some two-qubit states. We show that the two-qudit Greenberger-Horne-Zeilinger (GHZ) state with an arbitrary even d ≥ 2 exhibits perfect correlations/anticorrelations and belongs to the introduced two-qudit state class. These new results are important steps towards proving in general the 3/2 upper bound on quantum violation of the original Bell inequality. The latter would imply that similarly as the Tsirelson upper bound 2 √ 2 specifies the quantum analog of the CHSH inequality for all bipartite quantum states, the upper bound 3 2 specifies the quantum analog of the original Bell inequality for all bipartite quantum states with perfect correlations/ anticorrelations. Possible consequences for the experimental tests on violation of the original Bell inequality are briefly discussed.

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Section: Two-qudit States With Perfect Correlations/anticorrelationsmentioning

confidence: 99%

“…Independence of distributions Pa i (· |ω), P b k (·|ω) on setting of other measurements is referred to as Bell locality, see[15] for details.…”

mentioning

confidence: 99%

Quantum analog of the original Bell inequality for two-qudit states with perfect correlations/anticorrelations

Loubenets

Khrennikov

2019

J. Phys. A: Math. Theor.

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“…. · P N,s N (dλ N |ω)ν E S (dω) 4 For the general statements on the LHV modelling, see section 4 in [26].…”

Section: General N -Partite Bell Inequalitiesmentioning

confidence: 99%

Quantifying Tolerance of a Nonlocal Multi-Qudit State to Any Local Noise

Loubenets

2018

Entropy

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We present a general approach for quantifying tolerance of a nonlocal N-partite state to any local noise under different classes of quantum correlation scenarios with arbitrary numbers of settings and outcomes at each site. This allows us to derive new precise bounds in d and N on noise tolerances for: (i) an arbitrary nonlocal N-qudit state; (ii) the N-qudit Greenberger-Horne-Zeilinger (GHZ) state; (iii) the N-qubit W state and the N-qubit Dicke states, and to analyse asymptotics of these precise bounds for large N and d.

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“…More generally, quantum violation of any (unconditional) correlation bipartite Bell inequality cannot 2 exceed the real Grothendiek's constant K (R) G ∈ [1.676, 1.783] but this is not already the case for quantum violation of general [11] bipartite Bell inequalities, in particular, bipartite Bell inequalities on joint probabilities, and last years this problem was intensively discussed in the literature within different mathematical approaches [12,13,14,15,16,17,18,19,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

Violation of general Bell inequalities by a pure bipartite quantum state

Loubenets,

Namkung

2021

Preprint

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In the present article, based on the formalism introduced in [Loubenets, J. Math. Phys. 53, 022201 (2012)], we derive for a pure bipartite quantum state a new upper bound on its maximal violation of general Bell inequalities. This new bound indicates that, for an infinite dimensional pure bipartite state with a finite sum of its Schmidt coefficients, violation of any general Bell inequality is bounded from above by the value independent on a number of settings and a type of outcomes, continuous or discrete, specific to this Bell inequality. As an example, we apply our new general results to specifying upper bounds on the maximal violation of general Bell inequalities by infinite dimensional bipartite states having the Bell states like forms comprised of two binary coherent states |α , | − α , with α > 0. We show that, for each of these bipartite coherent states, the maximal violation of general Bell inequalities cannot exceed the value 3 and analyse numerically the dependence of the derived analytical upper bounds on a parameter α > 0.

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Bell’s Nonlocality in a General Nonsignaling Case: Quantitatively and Conceptually

Cited by 19 publications

References 41 publications

Quantum analog of the original Bell inequality for two-qudit states with perfect correlations/anticorrelations

Quantum analog of the original Bell inequality for two-qudit states with perfect correlations/anticorrelations

Quantifying Tolerance of a Nonlocal Multi-Qudit State to Any Local Noise

Violation of general Bell inequalities by a pure bipartite quantum state

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