The von Neumann Entropy of EPR Spin Correlation for the Relativistic Pairs

TL;DR

This paper investigates how the von Neumann entropy of EPR spin pairs varies under Lorentz transformations, revealing relativistic effects on quantum entanglement and particle distinguishability.

Contribution

It introduces a method to calculate the von Neumann entropy of relativistic EPR pairs from the reduced density matrix after Lorentz boosts, highlighting relativistic effects on quantum correlations.

Findings

Von Neumann entropy varies with Lorentz transformation.

Relativistic effects influence particle distinguishability.

Entropy behavior analyzed in super-relativistic limit.

Abstract

Variation of the von Neumann entropy by the Lorentz transformation is discussed. Taking the spin-singlet state in the center of mass frame, the von Neumann entropy in the laboratory frame is calculated from the reduced density matrix obtained by taking the trace over 4-momentum after the Lorentz transformation. As the model to discuss the EPR spin correlation, it is supposed that one parent particle splits into a superposition state of various pair states in various directions. Computing the von Neumann entropy and the Shannon entropy, we have shown a global behavior of the entropy to see a relativistic effect. We discuss also the super-relativistic limit, distinguishability between the two particles of the pair and so on.