Nonviolation of Bell's Inequality in Translation Invariant Systems

Abstract

The nature of quantum correlations in strongly correlated systems has been a subject of intense research. In particular, it has been realized that entanglement and quantum discord are present at quantum phase transitions and able to characterize it. Surprisingly, it has been shown for a number of different systems that qubit pairwise states, even when highly entangled, do not violate Bell's inequalities, being in this sense local. Here we show that such a local character of quantum correlations is in fact general for translation invariant systems and has its origins in the monogamy trade-off obeyed by tripartite Bell correlations. We illustrate this result in a quantum spin chain with a soft breaking of translation symmetry. In addition, we extend the monogamy inequality to the $N$-qubit scenario, showing that the bound increases with $N$ and providing examples of its saturation through uniformly generated random pure states.

Published erratum added at the end

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• Multi-partite quantum nonlocality and Bell-type inequalities in an infinite-order quantum phase transition of the one-dimensional spin-1/2 XXZ chain
• Complementarity between Tripartite Quantum Correlation and Bipartite Bell Inequality Violation in Three Qubit States
• Beating no-go theorems by engineering defects in quantum spin models
• Violation of Bell inequality in perfect translation invariant systems
• Bell-CHSH function approach to quantum phase transitions in matrix product systems
• Bounding the persistency of the nonlocality of W states
• Violation of the Bell inequality in quantum critical random spin-$1/2$ chains
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• Thermal entanglement in the mixed-spin Ising-Heisenberg double sawtooth frustrated ladder
• Trade-off relation among genuine three-qubit nonlocalities in four-qubit systems
• Bell-type correlation at quantum phase transitions in spin-1 chain
• Study of quantum non-locality by CHSH function and its extension in disordered fermions
• Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations