Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations
arXiv:2006.05537 · doi:10.1007/s13538-021-00998-1
Abstract
Using Bell-inequalities as a tool to explore non-classical physical behaviours, in this paper we analyze what one can expect to find in many-body quantum physics. Concretely, framing the usual correlation scenarios as a concrete spin-lattice, we want to know whether or not it is possible to violate a Bell-inequality restricted to this scenario. Using clustering theorems, we are able to show that a large family of quantum many-body systems behave almost locally, violating Bell-inequalities (if so) only by a non-significant amount. We also provide examples, explain some of our assumptions via counter-examples and present all the proofs for our theorems. We hope the paper is self-contained.
arXiv comment12 pages. 3 figures. Comments are welcome!
References in corpus (30)
- Bell nonlocality
- Spectral Gap and Exponential Decay of Correlations
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Propagation of Correlations in Quantum Lattice Systems
- Bell Correlations in a Bose-Einstein Condensate
- Detecting non-locality in multipartite quantum systems with two-body correlation functions
- Genuine quantum correlations in quantum many-body systems: a review of recent progress
- Large violation of Bell inequalities with low entanglement
- Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
- Locality of temperature
- Bell inequalities and entanglement at quantum phase transition in the XXZ Model
- Nonlocality and entanglement in the XY model
- On modifications of Reichenbach's principle of common cause in light of Bell's theorem
- Nonlocality in many-body quantum systems detected with two-body correlators
- Nonlocality and entanglement in qubit systems
- Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states
- Rapid mixing implies exponential decay of correlations
- Entanglement-ergodic quantum systems equilibrate exponentially well
- Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems
- Multipartite non-locality in a thermalized Ising spin-chain
- Nonviolation of Bell's Inequality in Translation Invariant Systems
- Energy as a detector of nonlocality of many-body spin systems
- Bounding the set of classical correlations of a many-body system
- Translationally invariant multipartite Bell inequalities involving only two-body correlators
- Bell correlations at Ising quantum critical points
- Entanglement and Nonlocality in Infinite 1D Systems
- Detecting many-body Bell non-locality by solving Ising models
- Bell scenarios in which nonlocality and entanglement are inversely related
- Bipartite nonlocality with a many-body system
- Violation of the Bell inequality in quantum critical random spin- chains