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

TL;DR

This paper investigates how genuine three-qubit EPR steering behaves under various environmental noises and introduces pre-processing techniques to reveal hidden steerability that noise alone cannot uncover.

Contribution

It demonstrates that local pre-processing can reveal or enhance hidden genuine steerability in three-qubit states affected by decoherence.

Findings

Genuine steerability decreases with more parties undergoing noise.

Steerability can revive after damping increases.

Pre-processing reveals hidden steerability not apparent from noise effects.

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 demonstrates genuine steering to Charlie. In both these scenarios, we analyze the genuine steerability of the generalized Greenberger-Horne-Zeilinger (gGHZ) states or the W-class states under the action of noise modeled 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, the hidden genuine steerability of a state cannot be revealed solely from the action of noise. So, the parties having a characterized 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.