Generic Bell correlation between arbitrary local algebras in quantum field theory
arXiv:math-ph/9909013 · doi:10.1063/1.533253
Abstract
We prove that for any two commuting von Neumann algebras of infinite type, the open set of Bell correlated states for the two algebras is norm dense. We then apply this result to algebraic quantum field theory -- where all local algebras are of infinite type -- in order to show that for any two spacelike separated regions, there is an open dense set of field states that dictate Bell correlations between the regions. We also show that any vector state cyclic for one of a pair of commuting nonabelian von Neumann algebras is entangled (i.e., nonseparable) across the algebras -- from which it follows that every field state with bounded energy is entangled across any two spacelike separated regions.
Third version; correction in the proof of Proposition 4
References in corpus (4)
- On the volume of the set of mixed entangled states
- Bell's inequalities and density matrices. Revealing hidden nonlocality.
- Continuity of symplectically adjoint maps and the algebraic structure of Hadamard vacuum representations for quantum fields on curved spacetime
- Bipartite Mixed States of Infinite-Dimensional Systems are Generically Nonseparable
Cited by in corpus (30)
- Quantum enhanced measurements without entanglement
- Entropy, entanglement, and area: analytical results for harmonic lattice systems
- Entanglement from the vacuum
- Violating Bell's inequalities in the vacuum
- Quantum Simulating Nature's Fundamental Fields
- On the quantification of entanglement in infinite-dimensional quantum systems
- Entanglement in indistinguishable particle systems
- Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and Reeh-Schlieder theorems
- Entanglement and Open Systems in Algebraic Quantum Field Theory
- Natural Entanglement in Bose-Einstein Condensates
- Distillability and positivity of partial transposes in general quantum field systems
- Einstein-Podolsky-Rosen correlations between two uniformly accelerated oscillators
- Long-range entanglement in the Dirac vacuum
- Relativistic quantum information and time machines
- Weakly coupled local particle detectors cannot harvest entanglement
- Reichenbach's Common Cause Principle in Algebraic Quantum Field Theory with Locally Finite Degrees of Freedom
- Noncommuting local common causes for correlations violating the Clauser-Horne inequality
- Remarks on Causality in Relativistic Quantum Field Theory
- Entanglement in Algebraic Quantum Mechanics: Majorana fermion systems
- Noncommutative Common Cause Principles in Algebraic Quantum Field Theory
- Entanglement Structures in Quantum Field Theories II: Distortions of Vacuum Correlations Through the Lens of Local Observers
- Wigner's inequalities in quantum field theory
- Entanglement beyond tensor product structure: algebraic aspects of quantum non - separability
- EPR states and Bell correlated states in algebraic quantum field theory
- Quantum physics, fields and closed timelike curves: The D-CTC condition in quantum field theory
- Entanglement, space-time and the Mayer-Vietoris theorem
- A State-Dependent Noncontextuality Inequality in Algebraic Quantum Theory
- Identification of a natural fieldlike entanglement resource in trapped-ion chains
- Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory
- Cluster property and Bell's inequalities