Degradation of non-maximal entanglement of scalar and Dirac fields in non-inertial frames

TL;DR

This paper studies how entanglement between scalar and Dirac fields degrades for accelerated observers due to the Unruh effect, revealing differences in entanglement behavior and information retention in non-inertial frames.

Contribution

It demonstrates the degradation patterns of entanglement in scalar and Dirac fields under acceleration, highlighting the inequivalence of Minkowski and Rindler quantizations.

Findings

Maximally entangled states are unaffected by degradation.

Scalar field entanglement becomes non-distillable at infinite acceleration.

Dirac field retains some entanglement even at infinite acceleration.

Abstract

The entanglement between two modes of the free scalar and Dirac fields as seen by two relatively accelerated observers has been investigated. It is found that the same initial entanglement for an initial state parameter $\alpha$ and its "normalized partner" $\sqrt{1-\alpha^{2}}$ will be degraded by the Unruh effect along two different trajectories except for the maximally entangled state, which just shows the inequivalence of the quantization for a free field in the Minkowski and Rindler coordinates. In the infinite acceleration limit the state doesn't have the distillable entanglement for any $\alpha$ for the scalar field but always remains entangled to a degree which is dependent of $\alpha$ for the Dirac field. It is also interesting to note that in this limit the mutual information equals to just half of the initially mutual information, which is independent of $\alpha$ and the type of field.