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:quant-ph/0602119 · Physical Review Letters

Test of Nonlocality for a Continuous-Variable State Based on an Arbitrary Number of Measurement Outcomes

Wonmin Son, Časlav Brukner, M. S. Kim

Published Sep 11, 2006• 17 citations
arXivHTMLPDF

Abstract

We propose a scheme to test Bell's inequalities for an arbitrary number of measurement outcomes on entangled continuous-variable (CV) states. The Bell correlation functions are expressible in terms of phase-space quasiprobability functions with complex ordering parameters, which can experimentally be determined via a local CV-qubit interaction. We demonstrate that CV systems can give higher violations of these Bell's inequalities than of the ones developed for two-outcome observables.

DOI
10.1103/physrevlett.97.110401

Related papers

High-dimensional Bell test for a continuous-variable state in phase space and its robustness to detection inefficiency

Seung-Woo Lee, Hyunseok Jeong

We propose a scheme for testing high-dimensional Bell inequalities in phase space. High-dimensional Bell inequalities can be recast into the forms of a phase-space version using quasiprobability functions with the complex-valued order parameter. We investigate their violations for two-mode squeezed states while increasing the dimension of measurement outcomes and finally show the robustness of high-dimensional tests to detection inefficiency.

arXiv:1006.4012•Physical Review A•Feb 10, 2011•4 citations

d-outcome measurement for a nonlocality test

Wonmin Son, Jinhyoung Lee, M S Kim

For the purpose of a nonlocality test, we propose a general correlation observable of two parties by utilizing local d -outcome measurements with SU ( d ) transformations and classical communications. Generic symmetries of the SU ( d ) transformations and correlation observables are found for the test of nonlocality. It is shown that these symmetries dramatically reduce the number of numerical variables, which is important for numerical analysis of nonlocality. A linear combination of the correlation observables, which is reduced to the Clauser–Horne–Shimony-Holt (CHSH) Bell's inequality for two outcome measurements, leads to the Collins–Gisin–Linden–Massar–Popescu (CGLMP) nonlocality test for d -outcome measurement. As a system to be tested for its nonlocality, we investigate a continuous-variable (CV) entangled state with d measurement outcomes. It allows the comparison of nonlocality based on different numbers of measurement outcomes on one physical system. In our example of the CV state, we find that a pure entangled state of any degree violates Bell's inequality for d (⩾2) measurement outcomes when the observables are of SU ( d ) transformations.

arXiv:quant-ph/0309193•Journal of Physics A Mathematical and General•Nov 25, 2004•20 citations

Bell inequalities for continuous-variable measurements

Qiongyi He, Eric G. Cavalcanti, M. D. Reid +1 more

Tests of local hidden-variable theories using measurements with continuous-variable (CV) outcomes are developed, and a comparison of different methods is presented. As examples, we focus on multipartite entangled Greenberger-Horne-Zeilinger and cluster states. We suggest a physical process that produces the states proposed here, and investigate experiments both with and without binning of the continuous variable. In the former case, the Mermin-Klyshko inequalities can be used directly. For unbinned outcomes, the moment-based Cavalcanti-Foster-Reid-Drummond inequalities are extended to functional inequalities by consideration of arbitrary functions of the measurements at each site. By optimizing these functions, we obtain more robust violations of local hidden-variable theories than with either binning or moments. Recent inequalities based on the algebra of quaternions and octonions are compared with these methods. Since the prime advantage of CV experiments is to provide a route to highly efficient detection via homodyne measurements, we analyze the effect of noise and detection losses in both binned and unbinned cases. The CV moment inequalities with an optimal function have greater robustness to both loss and noise. This could permit a loophole-free test of Bell inequalities.

arXiv:1005.2208•Physical Review A•Jun 9, 2010•35 citations

Quantum Nonlocality and Partial Transposition for Continuous-Variable Systems

Alejo Salles, Daniel Cavalcanti, Antonio Acín

A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced [Cavalcanti, Phys. Rev. Lett. 99, 210405 (2007)10.1103/PhysRevLett.99.210405]. We prove that any n-mode quantum state violating this inequality with quadrature measurements necessarily has a negative partial transposition. Our results thus establish the first link between nonlocality and bound entanglement for continuous-variable systems.

arXiv:0804.4703•Physical Review Letters•Jul 25, 2008•25 citations

Violations of entropic Bell inequalities with coarse-grained quadrature measurements for continuous-variable states

Zeng‐Bing Chen, Yao Fu, Yu-Kang Zhao

It is a long-standing belief, as pointed out by Bell in 1986, that it is impossible to use a two-mode Gaussian state possessing a positive-definite Wigner function to demonstrate nonlocality as the Wigner function itself provides a local hidden-variable model. In particular, when one performs continuous-variable (CV) quadrature measurements upon a routinely generated CV entanglement, namely, the two-mode squeezed vacuum (TMSV) state, the resulting Wigner function is positive-definite and as such, the TMSV state cannot violate any Bell inequality using CV quadrature measurements. We show here, however, that a Bell inequality for CV states in terms of entropies can be quantum mechanically violated by the TMSV state with two coarse-grained quadrature measurements per site within experimentally accessible parameter regime. The proposed CV entropic Bell inequality is advantageous for an experimental test, especially for a possible loophole-free test of nonlocality, as the quadrature measurements can be implemented with homodyne detections of nearly $100%$ detection efficiency under current technology.

arXiv:1409.0437•Physical Review A•Aug 26, 2014•5 citations

Quantum nonlocality test for continuous-variable states with dichotomic observables

Hyunseok Jeong, Wonmin Son, M. S. Kim +2 more

There have been theoretical and experimental studies on quantum nonlocality for continuous variables, based on dichotomic observables. In particular, we are interested in two cases of dichotomic observables for the light field of continuous variables: One case is even and odd numbers of photons and the other case is no photon and the presence of photons. We analyze various observables to give the maximum violation of Bell's inequalities for continuous-variable states. We discuss an observable which gives the violation of Bell's inequality for any entangled pure continuous-variable state. However, it does not have to be a maximally entangled state to give the maximal violation of Bell's inequality. This is attributed to a generic problem of testing the quantum nonlocality of an infinite-dimensional state using a dichotomic observable.

arXiv:quant-ph/0210110•Physical Review A•Jan 28, 2003•152 citations
We propose a scheme to test Bell's inequalities for an arbitrary number of measurement outcomes on entangled continuous-variable (CV) states. The Bell correlation functions are expressible in terms of phase-space quasiprobability functions with complex ordering parameters, which can experimentally be determined via a local CV-qubit interaction. We demonstrate that CV systems can give higher violations of these Bell's inequalities than of the ones developed for two-outcome observables.
For the purpose of a nonlocality test, we propose a general correlation observable of two parties by utilizing local d -outcome measurements with SU ( d ) transformations and classical communications. Generic symmetries of the SU ( d ) transformations and correlation observables are found for the test of nonlocality. It is shown that these symmetries dramatically reduce the number of numerical variables, which is important for numerical analysis of nonlocality. A linear combination of the correlation observables, which is reduced to the Clauser–Horne–Shimony-Holt (CHSH) Bell's inequality for two outcome measurements, leads to the Collins–Gisin–Linden–Massar–Popescu (CGLMP) nonlocality test for d -outcome measurement. As a system to be tested for its nonlocality, we investigate a continuous-variable (CV) entangled state with d measurement outcomes. It allows the comparison of nonlocality based on different numbers of measurement outcomes on one physical system. In our example of the CV state, we find that a pure entangled state of any degree violates Bell's inequality for d (⩾2) measurement outcomes when the observables are of SU ( d ) transformations.
Tests of local hidden-variable theories using measurements with continuous-variable (CV) outcomes are developed, and a comparison of different methods is presented. As examples, we focus on multipartite entangled Greenberger-Horne-Zeilinger and cluster states. We suggest a physical process that produces the states proposed here, and investigate experiments both with and without binning of the continuous variable. In the former case, the Mermin-Klyshko inequalities can be used directly. For unbinned outcomes, the moment-based Cavalcanti-Foster-Reid-Drummond inequalities are extended to functional inequalities by consideration of arbitrary functions of the measurements at each site. By optimizing these functions, we obtain more robust violations of local hidden-variable theories than with either binning or moments. Recent inequalities based on the algebra of quaternions and octonions are compared with these methods. Since the prime advantage of CV experiments is to provide a route to highly efficient detection via homodyne measurements, we analyze the effect of noise and detection losses in both binned and unbinned cases. The CV moment inequalities with an optimal function have greater robustness to both loss and noise. This could permit a loophole-free test of Bell inequalities.
A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced [Cavalcanti, Phys. Rev. Lett. 99, 210405 (2007)10.1103/PhysRevLett.99.210405]. We prove that any n-mode quantum state violating this inequality with quadrature measurements necessarily has a negative partial transposition. Our results thus establish the first link between nonlocality and bound entanglement for continuous-variable systems.
It is a long-standing belief, as pointed out by Bell in 1986, that it is impossible to use a two-mode Gaussian state possessing a positive-definite Wigner function to demonstrate nonlocality as the Wigner function itself provides a local hidden-variable model. In particular, when one performs continuous-variable (CV) quadrature measurements upon a routinely generated CV entanglement, namely, the two-mode squeezed vacuum (TMSV) state, the resulting Wigner function is positive-definite and as such, the TMSV state cannot violate any Bell inequality using CV quadrature measurements. We show here, however, that a Bell inequality for CV states in terms of entropies can be quantum mechanically violated by the TMSV state with two coarse-grained quadrature measurements per site within experimentally accessible parameter regime. The proposed CV entropic Bell inequality is advantageous for an experimental test, especially for a possible loophole-free test of nonlocality, as the quadrature measurements can be implemented with homodyne detections of nearly 100100%100 detection efficiency under current technology.
There have been theoretical and experimental studies on quantum nonlocality for continuous variables, based on dichotomic observables. In particular, we are interested in two cases of dichotomic observables for the light field of continuous variables: One case is even and odd numbers of photons and the other case is no photon and the presence of photons. We analyze various observables to give the maximum violation of Bell's inequalities for continuous-variable states. We discuss an observable which gives the violation of Bell's inequality for any entangled pure continuous-variable state. However, it does not have to be a maximally entangled state to give the maximal violation of Bell's inequality. This is attributed to a generic problem of testing the quantum nonlocality of an infinite-dimensional state using a dichotomic observable.