Spin quantum correlations of relativistic particles

Abstract

We show that a pair of massive relativistic spin-1/2 particles prepared in a maximally entangled spin state in general is not capable of maximally violating the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequalities without a post-selection of the particles momenta, representing a major difference in relation to non-relativistic systems. This occurs because the quantization axis of the measurements performed on each particle depends on the particle velocity, such that it is not possible to define a reduced density matrix for the particles spin. We also show that the amount of violation of the CHSH inequality depends on the reference frame, and that in some frames the inequality may not be violated.

4 pages, 3 figures. The introductory part has changed. More arguments against the definition of a reduced spin density matrix for a relativistic system are presented

References in corpus (5)

• Quantum Entanglement of Moving Bodies
• Lorentz-covariant reduced spin density matrix and EPR-Bohm correlations
• Lorentz-invariant Bell's inequality
• Relativistic-invariant quantum entanglement between the spins of moving bodies
• Physical interpretation of the Wigner rotations and its implications for relativistic quantum information

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• Relativistic Bell Test within Quantum Reference Frames
• Spin and localization of relativistic fermions and uncertainty relations
• Spin operator in the Dirac theory
• A new view on spin reduced density matrix for relativistic particles
• Wigner rotations and an apparent paradox in relativistic quantum information
• Spin Operator and Entanglement in Quantum Field Theory
• Relativistic Einstein-Podolsky-Rosen correlations and localization
• Relativistic spin operator must be intrinsic
• Lorentz transformations for massive two-particle systems: entanglement change and invariant subspaces
• Observer dependence of entanglement in "nonrelativistic" quantum mechanics
• Relativistic spin operator and Dirac equation
• One and two spin$-1/2$ particles systems under Lorentz transformations
• Localization POVMs and intrinsic temporal uncertainty
• The shadows of quantum gravity on Bell's inequality
• Information under Lorentz transformation
• Localised Systems in Relativistic Quantum Information
• Bundle Theoretic Descriptions of Massive Single-Particle State Spaces; With a view toward Relativistic Quantum Information Theory