Decoherence of Einstein-Podolsky-Rosen steering

TL;DR

This paper investigates how EPR steering correlations between two quantum systems decay under environmental coupling, revealing phenomena like sudden death of steering and directional effects influenced by thermal reservoirs.

Contribution

It provides a detailed analysis of the decoherence dynamics of EPR steering in different quantum states, including two-mode squeezed states and Schrödinger cat states, highlighting new directional effects.

Findings

Steering can abruptly vanish after finite time due to decoherence.

Decoherence effects depend on whether the reservoir is thermal or not.

Directional asymmetry in steering decay is observed under different reservoir conditions.

Abstract

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.