Violation of Bell inequalities by stochastic simulations of Gaussian States based on their positive Wigner representation

• URL: http://arxiv.org/abs/2006.15537v3
• Date: Sat, 30 Jan 2021 06:30:54 GMT
• Title: Violation of Bell inequalities by stochastic simulations of Gaussian States based on their positive Wigner representation
• Authors: Eric Lantz, Mehdi Mabed and Fabrice Devaux
• Abstract summary: We study the use of an everywhere positive Wigner function as a probability density to perform simulations in quantum optics. Because of the difference between symmetrically and normally ordered operators, some trajectories in simulations can imply negative intensities, despite a positive mean. For the case of the Clauser-Horn Bell inequality, the influence of the quantum efficiency of the detectors is studied.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: At first sight, the use of an everywhere positive Wigner function as a probability density to perform stochastic simulations in quantum optics seems equivalent to the introduction of local hidden variables, thus preventing any violation of Bell inequalities. However, because of the difference between symmetrically and normally ordered operators, some trajectories in stochastic simulations can imply negative intensities, despite a positive mean. Hence, Bell inequalities do not apply. Here, we retrieve for a weakly squeezed Gaussian state the maximum violation on polarization states allowed by quantum mechanics, for the Clauser-Horn-Shimony-Holt (CHSH), as well as for the Clauser-Horn Bell inequalities. For the case of the Clauser-Horn Bell inequality, the influence of the quantum efficiency of the detectors is studied, and for both inequalities, the influence of the degree of squeezing is assessed, as well as the uncertainty range versus the number of trajectories used in the simulations.

Related papers

• Nonlocality under Jaynes-Cummings evolution: beyond pseudospin operators [44.99833362998488]
  We re-visit the generation and evolution of (Bell) nonlocality in hybrid scenarios whose dynamics is determined by the Jaynes-Cummings Hamiltonian. Recent results on the optimal Bell violation in qubit-qudit systems show that the nonlocality is much greater than previously estimated.
  arXiv  Detail & Related papers  (2024-10-14T16:01:23Z)
• Numerical approach to the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory [0.0]
  The Bell-CHSH inequality is expressed in terms of the Lorentz invariant inner products of test functions. Violations of the Bell-CHSH inequality are reported for different values of the particle mass parameter.
  arXiv  Detail & Related papers  (2024-06-28T16:24:24Z)
• Robust self-testing of Bell inequalities tilted for maximal loophole-free nonlocality [1.099532646524593]
  quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors. We use a novel Jordan's lemma-based proof technique to obtain robust analytical self-testing statements for the entire family of tilted-Bell inequalities.
  arXiv  Detail & Related papers  (2024-05-14T16:31:06Z)
• Some consequences of Sica's approach to Bell's inequalities [55.2480439325792]
  Louis Sica derived Bell's inequalities from the hypothesis that the time series of outcomes observed in one station does not change if the setting in the other station is changed. In this paper, Sica's approach is extended to series with non ideal efficiency and to the actual time structure of experimental data.
  arXiv  Detail & Related papers  (2024-03-05T13:59:52Z)
• Optimizing Fictitious States for Bell Inequality Violation in Bipartite Qubit Systems [5.151248813215795]
  We show that if Bell inequality violation is observed with a fictitious state, then it implies the same for a quantum sub-state. We further show analytically that the basis which diagonalizes the spin-spin correlations is optimal for constructing fictitious states.
  arXiv  Detail & Related papers  (2023-11-15T18:05:44Z)
• Optimal variance-reduced stochastic approximation in Banach spaces [114.8734960258221]
  We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. We establish non-asymptotic bounds for both the operator defect and the estimation error.
  arXiv  Detail & Related papers  (2022-01-21T02:46:57Z)
• Spectral clustering under degree heterogeneity: a case for the random walk Laplacian [83.79286663107845]
  This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
  arXiv  Detail & Related papers  (2021-05-03T16:36:27Z)
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios [37.067444579637076]
  Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely. We present a new approach for quantum self-testing in Bell non-locality scenarios.
  arXiv  Detail & Related papers  (2021-04-27T08:15:01Z)
• Quantum Bell inequalities from Information Causality -- tight for Macroscopic Locality [0.34771439623170125]
  In a Bell test, the set of observed probability distributions complying with the principle of local realism is fully characterized by Bell inequalities. We present a family of inequalities, which approximate the set of quantum correlations in Bell scenarios where the number of settings or outcomes can be arbitrary.
  arXiv  Detail & Related papers  (2021-03-08T19:36:13Z)
• Class of Bell-Clauser-Horne inequalities for testing quantum nonlocality [11.367526341820643]
  We propose methods for the rearrangement and linear inequality to prove a large variety of Bell-CH inequalities. We also derive a set of Bell-CH inequalities by using these methods which can be violated in some quantum entangled states.
  arXiv  Detail & Related papers  (2021-01-07T08:25:21Z)
• Using Randomness to decide among Locality, Realism and Ergodicity [91.3755431537592]
  An experiment is proposed to find out, or at least to get an indication about, which one is false. The results of such experiment would be important not only to the foundations of Quantum Mechanics.
  arXiv  Detail & Related papers  (2020-01-06T19:26:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.