Bell-type inequalities for systems of relativistic vector bosons

Abstract

We perform a detailed analysis of the possible violation of various Bell-type inequalities for systems of vector boson-antiboson pairs. Considering the general case of an overall scalar state of the bipartite system, we identify two distinct classes of such states, and determine the joint probabilities of spin measurement outcomes for each them. We calculate the expectation values of the CHSH, Mermin and CGLMP inequalities and find that while the generalised CHSH inequality is not expected to be violated for any of the scalar states, in the case of the Mermin and CGLMP inequalities the situation is different -- these inequalities can be violated in certain scalar states while they cannot be violated in others. Moreover, the degree of violation depends on the relative speed of the two particles.

arXiv comment9 pages, 5 figures, accepted for publication in Quantum

References in corpus (36)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Significant-loophole-free test of Bell's theorem with entangled photons
• A strong loophole-free test of local realism
• Bell inequalities for arbitrarily high dimensional systems
• Quantum Entanglement of Moving Bodies
• Quantum entropy and special relativity
• Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles
• Demonstration of entanglement-by-measurement of solid state qubits
• Observer dependent entanglement
• Relativistic entanglement and Bell's inequality
• Relativistic entanglement of two massive particles
• Testing Bell inequalities in Higgs boson decays
• Relativistic Einstein-Podolsky-Rosen correlation and Bell's inequality
• Testing entanglement and Bell inequalities in $H\to ZZ$
• Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles
• Lorentz-covariant reduced spin density matrix and EPR-Bohm correlations
• Two roles of relativistic spin operators
• Einstein-Podolsky-Rosen correlations of Dirac particles - quantum field theory approach
• Relativistic-invariant quantum entanglement between the spins of moving bodies
• Laboratory-frame tests of quantum entanglement in $H\to WW$
• Physical interpretation of the Wigner rotations and its implications for relativistic quantum information
• What is the relativistic spin operator?
• Position and spin in relativistic quantum mechanics
• Strange behavior of the relativistic Einstein-Podolsky-Rosen correlations
• Spin quantum correlations of relativistic particles
• Relativistic Bell Test within Quantum Reference Frames
• Spin and localization of relativistic fermions and uncertainty relations
• Einstein-Podolsky-Rosen correlations of vector bosons
• Global Dirac bispinor entanglement under Lorentz boosts
• Helicity correlations of vector bosons
• A new view on spin reduced density matrix for relativistic particles
• Entanglement of two relativistic particles with discrete momenta
• Relativistic massive particle with spin-1/2, a vector bundle point of view
• Relativistic Einstein-Podolsky-Rosen correlations and localization
• Relativistic spin operator must be intrinsic
• Single particle entanglement in the mid-and ultra-relativistic regime

Cited by in corpus (23)

• Observation of quantum entanglement in top quark pair production in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• When the Machine Chimes the Bell: Entanglement and Bell Inequalities with Boosted $t\bar{t}$
• Entanglement and Bell inequalities violation in $H\to ZZ$ with anomalous coupling
• Entanglement in flavored scalar scattering
• Optimizing Entanglement and Bell Inequality Violation in Top Anti-Top Events
• From angular coefficients to quantum observables: a phenomenological appraisal in di-boson systems
• Three-body Entanglement in Particle Decays
• Entanglement and Bell nonlocality with bottom-quark pairs at hadron colliders
• Quantum properties of $H\to V{V}^{\ast }$: precise predictions in the SM and sensitivity to new physics
• Quantum tomography of helicity states for general scattering processes
• Polarized ZZ pairs in gluon fusion and vector boson fusion at the LHC
• Entanglement and Bell inequality violation in vector diboson systems produced in decays of spin-0 particles
• Quantum State-Channel Duality for the calculation of Standard Model scattering amplitudes
• Spin correlations and Bell nonlocality in $\Lambda \bar{\Lambda }$ pair production from $e^{+}{e}^{-}$ collisions with a thrust cut
• Entropic uncertainty relations and quantum Fisher information of top quarks in a large hadron collider
• Polarized-boson pairs at NLO in the SMEFT
• Three-Body Non-Locality in Particle Decays
• Entanglement features in scattering mediated by heavy particles
• Qubit entanglement from forward scattering
• Thomas--Wigner rotation as a holonomy for spin-$1/2$ particles
• Non-Heisenbergian quantum mechanics
• Colliders are not Testing Locality via Bell's Inequality nor Providing an Unconditional Proof of Entanglement
• Proposal for an experiment to verify Wigner's rotation at non-relativistic speeds with massive spin-$1/2$ particles