Reexamination of a multisetting Bell inequality for qudits

Yeong Cherng Liang, Chu Wee Lim, Dong Ling Deng

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)

Abstract

The class of d -setting, d -outcome Bell inequalities proposed by Ji and co-workers are reexamined. For every positive integer d>2, we show that the corresponding nontrivial Bell inequality for probabilities provides the maximum classical winning probability of the Clauser-Horne-Shimony-Holt-like game with d inputs and d outputs. We also demonstrate that the general classical upper bounds given by Ji are underestimated, which invalidates many of the corresponding correlation inequalities presented thereof. We remedy this problem, partially, by providing the actual classical upper bound for d≤13 (including nonprime values of d). We further determine that for prime value d in this range, most of these probability and correlation inequalities are tight, i.e., facet-inducing for the respective classical correlation polytope. Stronger lower and upper bounds on the quantum violation of these inequalities are obtained. In particular, we prove that once the probability inequalities are given, their correlation counterparts given by Ji and co-workers are no longer relevant in terms of detecting the entanglement of a quantum state.

Original languageEnglish
Article number052116
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume80
Issue number5
DOIs
Publication statusPublished - 2009 Nov 25

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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