Relativity of mixed entangled states

TL;DR

This paper investigates how relativistic effects, such as Lorentz transformations and acceleration, influence the entanglement and distillability of mixed quantum states, revealing that these properties are frame-dependent.

Contribution

It provides necessary and sufficient conditions for separability and distillability of mixed entangled states in relativistic settings, including effects of acceleration and Lorentz transformations.

Findings

Distillability depends on the observer's frame of reference.

In infinite acceleration, scalar field states lose distillable entanglement.

Dirac field states retain finite entanglement at infinite acceleration.

Abstract

We obtain the necessary and sufficient separability and distillability conditions of mixtures of a maximally entangled state and the completely separable state in relativistic setting. In an inertial frame we study the entanglement under Wigner rotations induced by Lorentz transformations. We also investigate the mixed state entanglement of scalar and Dirac fields as seen by two relatively accelerated observers. For scalar field we show that in infinite acceleration limit the state has no longer distillable entanglement. For dirac field the entanglement in the infinite acceleration limit is finite. In both cases we show that there are states that will change from entangled into separable for a certain value of velocity or acceleration. We conclude that distillability is a relative concept, depending on the frame in which it is observed.