Genuine three qubit Einstein–Podolsky–Rosen steering under decoherence: revealing hidden genuine steerability via pre-processing

Abstract

The behaviour of genuine EPR steering of three qubit states under various environmental noises is investigated. In particular, we consider the two possible steering scenarios in the tripartite setting:(1 → 2), where Alice demonstrates genuine steering to Bob-Charlie and (2 → 1), where Alice-Bob together demonstrate genuine steering to Charlie. In both these scenarios, we analyse the genuine steerability of the generalised Greenberger-Horne-Zeilinger (gGHZ) states or the W-class states under the action of noise modelled by amplitude damping (AD), phase flip (PF), bit flip (BF) and phase damping (PD) channels. In each case, we consider three different interactions with the noise depending upon the number of parties undergoing decoherence. We observed that the tendency to demonstrate genuine steering decreases as the number of parties undergoing decoherence increases from one to three. We have observed several instances where the genuine steerability of the state revives after collapsing if one keeps on increasing the damping. However, hidden genuine steerability of a state cannot be revealed solely from the action of noise. So, the parties having a characterised subsystem, perform local pre-processing operations depending upon the steering scenario and the state shared with the dual intent of revealing hidden genuine steerability or enhancing it.