Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1501.02582 · Physica Scripta

Quantum tomography and nonlocality

Evgeny V Shchukin, Stefano Mancini

Published Jun 1, 2015• 1 citation
arXivHTMLPDF

Abstract

We present a tomographic approach to the study of quantum nonlocality in multipartite systems. Bell inequalities for tomograms belonging to a generic tomographic scheme are derived by exploiting tools from convex geometry. Then, possible violations of these inequalities are discussed in specific tomographic realizations providing some explicit examples.

DOI
10.1088/0031-8949/90/7/074019

Related papers

A tomographic approach to quantum nonlocality

Stefano Mancini, Vladimir I. Man’ko, Evgeny V Shchukin +1 more

We propose a tomographic approach to study quantum nonlocality in continuous variable quantum systems. On one hand we derive a Bell-like inequality for measured tomograms. On the other hand, we introduce pseudospin operators whose statistics can be inferred from the data characterizing the reconstructed state, thus giving the possibility to use standard Bell's inequalities. Illuminating examples are also discussed.

arXiv:quant-ph/0302089•Journal of Optics B Quantum and Semiclassical Optics•Jun 1, 2003•16 citations

Bell's inequalities in the tomographic representation

Cosmo Lupo, V I Man'ko, G Marmo

The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be the most natural one to compare the predictions of classical and quantum theory. Examples of inequalities for two qubits an two qutrits are considered in the tomographic probability representation of spin states.

arXiv:quant-ph/0607059•Journal of Physics A Mathematical and General•Sep 19, 2006•14 citations

Bell's inequalities in the tomographic representation

Cosmo Lupo, Vladimir I. Man’ko, Giuseppe Marmo

The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be the most natural one to compare the predictions of classical and quantum theory. Examples of inequalities for two qubits an two qutrits are considered in the tomographic probability representation of spin states.

•Jan 1, 2006•14 citations

General Bell-CHSH type and entropic inequalities based on quantum tomograms

Loran V. Akopyan, Vladimir I. Man’ko

Review of Bell-CHSH type and entropic inequalities in composite quantum correlated systems in the probability representation of states is presented. The upper bounds for some new Bell-CHSH type inequalities within the framework of classical probability theory and in quantum tomography are compared. Violation of Bell-CHSH type inequalities are shown explicitly using the method of averaging in tomographic picture of quantum states. Joint tomographic entropies of multiqubit systems are studied. Limitations on inequalities for tomographic entropies are obtained. A negative result of possible connection between the violation of entropic and Bell-CHSH type inequalities in multi-partite states is reported.

Optics and Spectroscopy•Oct 1, 2011•0 citations

Bell-type inequalities and upper bounds of multi-qudit states

Loran V. Akopyan, Vladimir I. Man’ko

Multi-qudit systems are studied in tomographic probability representations of quantum qudit states. Results of calculations for Bell-type numbers within the framework of classical probability theory and in quantum tomography are compared. Violation of Bell-type inequalities are shown explicitly using the method of averaging in tomographic picture of quantum states.

arXiv:0906.5455•Jun 30, 2009•0 citations

Detecting Genuine Multipartite Quantum Nonlocality: A Simple Approach and Generalization to Arbitrary Dimensions

Jean-Daniel Bancal, Nicolas Brunner, Nicolas Gisin +1 more

The structure of Bell-type inequalities detecting genuine multipartite nonlocality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichny's original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite nonlocality in scenarios involving an arbitrary number of parties and systems of arbitrary dimension. Finally, we discuss the tightness and quantum mechanical violations of these inequalities.

arXiv:1011.0089•Physical Review Letters•Jan 11, 2011•169 citations
We present a tomographic approach to the study of quantum nonlocality in multipartite systems. Bell inequalities for tomograms belonging to a generic tomographic scheme are derived by exploiting tools from convex geometry. Then, possible violations of these inequalities are discussed in specific tomographic realizations providing some explicit examples.
Review of Bell-CHSH type and entropic inequalities in composite quantum correlated systems in the probability representation of states is presented. The upper bounds for some new Bell-CHSH type inequalities within the framework of classical probability theory and in quantum tomography are compared. Violation of Bell-CHSH type inequalities are shown explicitly using the method of averaging in tomographic picture of quantum states. Joint tomographic entropies of multiqubit systems are studied. Limitations on inequalities for tomographic entropies are obtained. A negative result of possible connection between the violation of entropic and Bell-CHSH type inequalities in multi-partite states is reported.
The structure of Bell-type inequalities detecting genuine multipartite nonlocality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichny's original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite nonlocality in scenarios involving an arbitrary number of parties and systems of arbitrary dimension. Finally, we discuss the tightness and quantum mechanical violations of these inequalities.