Genuine Einstein-Podolsky-Rosen steering of three-qubit states by multiple sequential observers

TL;DR

This paper explores how multiple sequential observers can demonstrate genuine tripartite EPR steering using a single three-qubit state, revealing limits based on state type and measurement sharpness.

Contribution

It introduces a framework for analyzing multiple sequential EPR steering demonstrations in three-qubit states, providing upper bounds for observers and comparing GHZ and W states.

Findings

GHZ states support more observers for EPR steering than W states.

(1->2) steering persists over a larger range of measurement sharpness.

Upper limits on observers vary with state type and measurement settings.

Abstract

We investigate the possibility of multiple use of a single copy of three-qubit states for genuine tripartite Einstein-Podolsky-Rosen (EPR) steering. A pure three-qubit state of either the Greenberger-Horne-Zeilinger (GHZ)-type or W-type is shared between two fixed observers in two wings and a sequence of multiple observers in the third wing who perform unsharp or non-projective measurements. The choice of measurement settings for each of the multiple observers in the third wing is independent and uncorrelated with the measurement settings and outcomes of the previous observers. We investigate all possible types of (2->1) and (1->2) genuine tripartite steering in the above set-up. For each case, we obtain an upper limit on the number of observers on the third wing who can demonstrate genuine EPR steering through violation of a tripartite steering inequality. We show that the GHZ state allows for a higher number of observers compared to that for W state. Additionally, (1->2) steering is possible for a larger range of the sharpness parameter compared to that for the (2->1) steering cases.