We consider two systems A and B that share Einstein-Podolsky-Rosen (EPR) steering correlations and study how these correlations will decay, when each of the systems are independently coupled to a reservoir. EPR steering is a directional form of entanglement, and the measure of steering can change depending on whether the system A is steered by B, or vice versa. First, we examine the decay of the steering correlations of the two-mode squeezed state. We find that if the system B is coupled to a reservoir, then the decoherence of the steering of A by B is particularly marked, to the extent that there is a sudden death of steering after a finite time. We find a different directional effect, if the reservoirs are thermally excited. Second, we study the decoherence of the steering of a Schr\"odinger cat state, modeled as the entangled state of a spin and harmonic oscillator, when the macroscopic system (the cat) is coupled to a reservoir.
@article{arxiv.1508.06383,
title = {Decoherence of Einstein-Podolsky-Rosen steering},
author = {L. Rosales-Zárate and R. Y. Teh and S. Kiesewetter and A. Brolis and K. Ng and M. D. Reid},
journal= {arXiv preprint arXiv:1508.06383},
year = {2015}
}