D-outcome measurement for a nonlocality test

Abstract

For the purpose of the 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, is led 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 $d(\ge 2)$ measurement outcomes when the observables are of SU($d$) transformations.

16 pages, 2 figures

References in corpus (11)

• Bell inequalities for arbitrarily high dimensional systems
• Violations of local realism by two entangled quNits are stronger than for two qubits
• Nonlocality of Einstein-Podolsky-Rosen State in Wigner Representation
• Quantum non-locality in two three-level systems
• Maximal Violation of Bell's Inequalities for Continuous Variable Systems
• Quantum nonlocality test for continuous-variable states with dichotomic observables
• Dynamics of Nonlocality for A Two-Mode Squeezed State in Thermal Environment
• Optimal Non-Universally Covariant Cloning
• A Zoology of Bell inequalities resistant to detector inefficiency
• Extremal equation for optimal completely-positive maps
• Correspondence between continuous variable and discrete quantum systems of arbitrary dimensions

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