Relativity of mixed entangled states

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.