Maximal violation of Bell inequalities by position measurements

We specify the local quasi hidden variable (LqHV) model reproducing the probabilistic description of all N-partite joint von Neumann measurements on an N-qudit state. Via this local probability model, we derive a new upper bound on the maximal violation by an N-qudit state of Bell inequalities of any type (either on correlation functions or on joint probabilities) for [Formula: see text] observables per site. This new upper bound not only improves for all [Formula: see text] [Formula: see text] and d the corresponding results available for general Bell inequalities in the literature but also, for the N-qubit case with two observables per site, reduces exactly to the attainable upper bound known for quantum violations of correlation [Formula: see text] setting Bell inequalities in a dichotomic case.

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Computing the Maximal Violation of Bell Inequalities for Multipartite Qubit via Partially Symmetric Tensor

International Journal of Theoretical Physics ◽

10.1007/s10773-019-04009-7 ◽

2019 ◽

Vol 58 (4) ◽

pp. 1161-1171

Author(s):

Lei Li ◽

Yan-nan Chen ◽

Ming Li ◽

Qing-wen Wang ◽

Li-qun Qi

Keyword(s):

Bell Inequalities ◽

Symmetric Tensor ◽

Maximal Violation ◽

Partially Symmetric

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Maximal violation of Bell inequalities for mixed states

Physical Review Letters ◽

10.1103/physrevlett.68.3259 ◽

1992 ◽

Vol 68 (22) ◽

pp. 3259-3261 ◽

Cited By ~ 280

Author(s):

Samuel L. Braunstein ◽

A. Mann ◽

M. Revzen

Keyword(s):

Bell Inequalities ◽

Mixed States ◽

Maximal Violation

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Maximal violation of tight Bell inequalities for maximal high-dimensional entanglement

Physical Review A ◽

10.1103/physreva.80.010103 ◽

2009 ◽

Vol 80 (1) ◽

Cited By ~ 17

Author(s):

Seung-Woo Lee ◽

Dieter Jaksch

Keyword(s):

Bell Inequalities ◽

High Dimensional ◽

Maximal Violation

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Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

Science Advances ◽

10.1126/sciadv.abc3847 ◽

2021 ◽

Vol 7 (7) ◽

pp. eabc3847

Author(s):

Armin Tavakoli ◽

Máté Farkas ◽

Denis Rosset ◽

Jean-Daniel Bancal ◽

Jedrzej Kaniewski

Keyword(s):

Quantum Key Distribution ◽

Random Number ◽

Random Number Generation ◽

Bell Inequalities ◽

Extremal Point ◽

Optimal Rate ◽

Quantum Nonlocality ◽

Space Structures ◽

Mutually Unbiased Bases ◽

Practical Relevance

Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by (i) introducing families of Bell inequalities that are maximally violated by d-dimensional MUBs and SICs, respectively, (ii) proving device-independent certification of natural operational notions of MUBs and SICs, and (iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device-independent quantum key distribution and device-independent quantum random number generation, respectively. Moreover, we also present the first example of an extremal point of the quantum set of correlations that admits physically inequivalent quantum realizations. Our results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.

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Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures

Scientific Reports ◽

10.1038/s41598-021-93786-5 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Marcin Wieśniak

Keyword(s):

Communication Complexity ◽

Quantum Communication ◽

Bell Inequality ◽

Bell Inequalities ◽

Quantum Correlations ◽

Complexity Reduction ◽

Main Difficulty ◽

Quantum Communication Complexity ◽

Number Of Particles ◽

Dicke States

AbstractQuantum correlations, in particular those, which enable to violate a Bell inequality, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles N. In case of Dicke states, we show that persistency can reach 0.482N, significantly more than reported in previous studies.

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