# On the largest Bell violation attainable by a quantum state

@article{Palazuelos2012OnTL,
title={On the largest Bell violation attainable by a quantum state},
author={Carlos Palazuelos},
journal={arXiv: Quantum Physics},
year={2012}
}
• C. Palazuelos
• Published 16 June 2012
• Mathematics
• arXiv: Quantum Physics
Multipartite Entanglement Detection Via Projective Tensor Norms
• Computer Science
Annales Henri Poincaré
• 2022
This work introduces and study a class of entanglement criteria based on the idea of applying local contractions to an input multipartite state, and then computing the projective tensor norm of the output, which allows for systematic relations between the performance of these two criteria.
Quantum communication complexity advantage implies violation of a Bell inequality
• Physics
Proceedings of the National Academy of Sciences
• 2016
It is proved that any large advantage over the best known classical strategy makes use of Bell nonlocal correlations, providing the missing link to the fundamental equivalence between Bell nonlocality and quantum advantage.
Restriction on the local realism violation in three-qubit states and its relation with tripartite entanglement
This work describes the states which give the extremal quantum values of a Bell-type inequality for a given value of the tripartite entanglement and shows that such extremal states can be reached if one introduced an appropriate order induced by the three-πEntanglement measure.
On the existence of a local quasi hidden variable (LqHV) model for each N-qudit state and the maximal quantum violation of Bell inequalities
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
New concise upper bounds on quantum violation of general multipartite Bell inequalities
The LqHV mathematical framework allows us to derive for all d and N a new upper bound on the maximal violation by an N-qudit state of all general Bell inequalities, and for some S, d, and N, the new upper bounds are attainable.
Quantum bounds on multiplayer linear games and device-independent witness of genuine tripartite entanglement
• Computer Science
• 2016
A systematic method is presented to derive device-independent witnesses of genuine tripartite entanglement, and to show in a simple manner that any nontrivial functional box, that could lead to trivialization of communication complexity in a multiparty scenario, cannot be realized in quantum mechanics.
Random Constructions in Bell Inequalities: A Survey
The aim of the present work is to review some of the recent results in this direction by focusing on the main ideas and removing most of the technical details, to make the previous study more accessible to a wide audience.
Multipartite entanglement in XOR games
• Mathematics
Quantum Inf. Comput.
• 2013
It is shown that the multipartite entangled states that are most often seen in today's literature can only lead to a bias that is a constant factor larger than the classical bias, which has the following surprising consequence: classical three-player XOR games do not follow an XOR parallel repetition theorem, even a very weak one.
Quantum steerability: Characterization, quantification, superactivation, and unbounded amplification
• Physics
• 2016
Quantum steering, also called Einstein-Podolsky-Rosen steering, is the intriguing phenomenon associated with the ability of spatially separated observers to steer---by means of local
More nonlocality with less entanglement in Clauser-Horne-Shimony-Holt experiments using inefficient detectors
• Computer Science
Physical Review A
• 2018
It is shown that the CHSH Inequality can always be violated for any nonzero detection efficiency and any choice of non-commuting measurements.

## References

SHOWING 1-10 OF 44 REFERENCES
Large Violation of Bell Inequalities with Low Entanglement
• Mathematics
• 2011
In this paper we obtain violations of general bipartite Bell inequalities of order $${\frac{\sqrt{n}}{\log n}}$$ with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct
Unbounded Violation of Tripartite Bell Inequalities
• Mathematics
• 2007
We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence
Semi-device-independent bounds on entanglement
• Computer Science
• 2011
It is shown that Bell-type inequalities are not only useful in verifying the presence of entanglement but can also be used to bound theEntanglement of the underlying physical system.
Near-Optimal and Explicit Bell Inequality Violations
• Physics
2011 IEEE 26th Annual Conference on Computational Complexity
• 2011
Two new two-player games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work are given.
Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory
• Mathematics
• 2010
In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $${{\rm \Omega} \left(\frac{\sqrt{n}}{\log^2n} \right)}$$
An anomaly of non-locality
• Physics
Quantum Inf. Comput.
• 2007
This work reviews the present knowledge on this anomaly, points out that Hardy's theorem has the same feature, and discusses the perspectives opened by these discoveries.
More nonlocality with less entanglement
• Physics
• 2011
Recent numerical investigations [K. Pal and T. Vertesi, Phys. Rev. A 82, 022116 (2010)] suggest that the I3322 inequality, arguably the simplest extremal Bell inequality after the CHSH inequality,
Local quasi hidden variable modelling and violations of Bell-type inequalities by a multipartite quantum state
We introduce for a general correlation scenario a new simulation model, a local quasi hidden variable (LqHV) model, where locality and the measure-theoretic construction inherent to a local hidden
The Unique Games Conjecture with Entangled Provers is False
• Computer Science
Algebraic Methods in Computational Complexity
• 2007
We consider one-round games between a classical verifier and two provers who share entanglement. We show that when the constraints enforced by the verifier are ‘unique’ constraints (i.e.,
Superactivation of quantum nonlocality.
In this Letter we show that quantum nonlocality can be superactivated. That is, one can obtain violations of Bell inequalities by tensorizing a local state with itself. In the second part of this