Using Weyl operators to study Mermin's inequalities in Quantum Field Theory
arXiv:2312.06918 · doi:10.1103/PhysRevD.109.045020
Abstract
Mermin's inequalities are investigated in a Quantum Field Theory framework by using von Neumann algebras built with Weyl operators. We devise a general construction based on the Tomita-Takesaki modular theory and use it to compute the vacuum expectation value of the Mermin operator, analyzing the parameter space and explicitly exhibiting a violation of Mermin's inequalities. Therefore, relying on the power of modular operators, we are able to demonstrate that Mermin's inequalities are violated when examined within the vacuum state of a scalar field theory.
arXiv comment8 pages, 1 figure, revised version. Accepted for publication in PRD
References in corpus (34)
- Quantum entanglement
- Three qubits can be entangled in two inequivalent ways
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
- Persistent entanglement in arrays of interacting particles
- Violation of Bell's inequality under strict Einstein locality conditions
- Significant-loophole-free test of Bell's theorem with entangled photons
- Observation of three-photon Greenberger-Horne-Zeilinger entanglement
- Bell violation with entangled photons, free of the fair-sampling assumption
- Advances in High Dimensional Quantum Entanglement
- Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
- Notes on Some Entanglement Properties of Quantum Field Theory
- Generation of Three-Qubit Entangled States using Superconducting Phase Qubits
- Bell inequality, Bell states and maximally entangled states for n qubits
- Experimental Test of Quantum Nonlocality in Four-photon Greenberger-Horne-Zeilinger Entanglement
- Entanglement and quantum tomography with top quarks at the LHC
- Experimental Verification of Multipartite Entanglement in Quantum Networks
- Experimental test of Mermin inequalities on a 5-qubit quantum computer
- Experimental Three-Particle Quantum Nonlocality under Strict Locality Conditions
- Quantum tops at the LHC: from entanglement to Bell inequalities
- Quantum information with top quarks in QCD
- Violating Bell's inequality with remotely-connected superconducting qubits
- Quantum discord and steering in top quarks at the LHC
- Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles
- Entanglement measures and their properties in quantum field theory
- Experimental demonstration of the violations of Mermin's and Svetlichny's inequalities for W- and GHZ-class of states
- Operational approach to Bell inequalities: applications to qutrits
- Maximal violation of the Bell-Clauser-Horne-Shimony-Holt inequality via bumpified Haar wavelets
- Weyl operators, Tomita-Takesaki theory, and Bell-Clauser-Horne-Shimony-Holt inequality violations
- Remarks on the Clauser-Horne-Shimony-Holt inequality in relativistic quantum field theory
- Are observables necessarily Hermitian?
- On the Feynman path integral formulation of the Bell-Clauser-Horne-Shimony-Holt inequality in Quantum Field Theory
- Mermin's inequalities in Quantum Field Theory
- BRST invariant formulation of the Bell-CHSH inequality in gauge field theories
- Probing Mermin's inequalities violations through pseudospin operators