Bell correlations at Ising quantum critical points

Abstract

When a collection of distant observers share an entangled quantum state, the statistical correlations among their measurements may violate a many-body Bell inequality, demonstrating a non-local behavior. Focusing on the Ising model in a transverse-field with power-law ($1/r^{\alpha }$) ferromagnetic interactions, we show that a permutationally invariant Bell inequality based on two-body correlations is violated in the vicinity of the quantum-critical point. This observation, obtained via analytical spin-wave calculations and numerical density-matrix renormalization group computations, is traced back to the squeezing of collective-spin fluctuations generated by quantum-critical correlations. We observe a maximal violation for infinite-range interactions ($\alpha =0$), namely when interactions and correlations are themselves permutationally invariant.

arXiv comment5 pages, 3 figures. Published version

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• The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing
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• Detecting Bell correlations in multipartite non-Gaussian spin states
• Robustness of non-locality in many-body open quantum systems
• Detection of quantum phase transition in spin-1 chain through multipartite high-order correlations
• Inherent quantum resources in stationary spin chains
• Deriving three-outcome permutationally invariant Bell inequalities
• Probing quantum entanglement from magnetic-sublevels populations: beyond spin squeezing inequalities
• Bell-type correlation at quantum phase transitions in spin-1 chain
• Persistent nonlocality in an ultracold-atom environment
• Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations
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