Violation of Bell inequality in perfect translation invariant systems

Abstract

Bell inequalities and nonlocality have been widely studied in one-dimensional quantum systems. As a kind of quantum correlation, it is expected that bipartite nonlocaity should be present in quantum systems, just as bipartite entanglement does. Surprisingly, for various models, two-qubit states do not violate Bell inequalities, i.e., they are local. Recently, it is realized that the results are related to the monogamy trade-off obeyed by bipartite Bell correlations, thus it is believed that for general translation invariant systems, two-qubit states should not violate the Bell inequality(Oliveira, EPL 100, 60004 (2012)). In this report, we will demonstrate that in perfect translation invariant systems, the Bell inequality can be violated. A nontrivial model is constructed to confirm the conclusion.

References in corpus (7)

• Quantum discord and quantum phase transition in spin chains
• Are general quantum correlations monogamous?
• Bell inequalities and entanglement at quantum phase transition in the XXZ Model
• Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems
• Critical Point Estimation and Long-Range Behavior in the One-Dimensional XY Model Using Thermal Quantum and Total Correlations
• Nonviolation of Bell's Inequality in Translation Invariant Systems
• Bell-CHSH function approach to quantum phase transitions in matrix product systems

Cited by in corpus (7)

• Monogamy of quantum correlations - a review
• Nonviolation of Bell's Inequality in Translation Invariant Systems
• Multi-partite quantum nonlocality and Bell-type inequalities in an infinite-order quantum phase transition of the one-dimensional spin-1/2 XXZ chain
• Beating no-go theorems by engineering defects in quantum spin models
• Violation of the Bell inequality in quantum critical random spin-$1/2$ chains
• Trade-off relation among genuine three-qubit nonlocalities in four-qubit systems
• Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements