Degradation of nonmaximal entanglement of scalar and Dirac fields in noninertial frames

Qiyuan Pan,Jiliang Jing

doi:10.1103/physreva.77.024302

Abstract

The entanglement between two modes of 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 $\ensuremath{\alpha}$ and its ``normalized partner'' $\sqrt{1\ensuremath{-}{\ensuremath{\alpha}}^{2}}$ 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 Minkowski and Rindler coordinates. In the infinite-acceleration limit, the state does not have distillable entanglement for any $\ensuremath{\alpha}$ for the scalar field, but always remains entangled to a degree that is dependent on $\ensuremath{\alpha}$ for the Dirac field. It is also interesting to note that in this limit the mutual information equals just half of the initial mutual information; this result is independent of $\ensuremath{\alpha}$ and the type of field.

Highlights

The entanglement between two modes of the free scalar and Dirac fields as seen by two relatively accelerated observers has been investigated
√ where α is some real number which satisfies |α| ∈ (0, 1), α and 1 − α2 are the so-called “normalized partners”, we will try to see what effects this uncertainly initial entangled state will on the degradation of entanglement for two relatively accelerated observers due to the presence of an initial state parameter α
In the infinite acceleration limit, the mutual information converges to the same value again, i.e., Ibf = −[α2 log2 α2 + (1 − α2) log2(1 − α2)], which equals to just half of Ibi

Summary

Introduction

The entanglement between two modes of the free scalar and Dirac fields as seen by two relatively accelerated observers has been investigated. This mixed state is always entangled for any finite acceleration of Bob. In the limit r → ∞, the negative eigenvalue will go to zero. The monotonous decrease of N (ρAB) with increasing r for different α means that the entanglement of the initial state is lost to the thermal fields generated by the Unruh effect.

Results

Conclusion