Distillation of genuine tripartite Einstein-Podolsky-Rosen steering

TL;DR

This paper demonstrates that perfectly genuine tripartite EPR steerable assemblages can be distilled from partially steerable ones in both one-sided and two-sided device-independent scenarios, with high efficiency even using few copies.

Contribution

It introduces protocols for distilling perfect tripartite EPR steerable assemblages from partial ones in hybrid scenarios, advancing quantum steering applications.

Findings

Distillation of perfect tripartite EPR steerable assemblages from partial ones.

High efficiency of distillation with few initial copies.

Applicability to GHZ and W states in practical scenarios.

Abstract

We show that a perfectly genuine tripartite EPR steerable assemblage can be distilled from partially genuine tripartite EPR steerable assemblages. In particular, we consider two types of hybrid scenarios: one-sided device-independent (1SDI) scenario (where one observer is untrusted, and other two observers are trusted) and two-sided device-independent (2SDI) scenario (where two observers are untrusted, and one observer is trusted). In both the scenarios, we show distillation of perfectly genuine steerable assemblage of three-qubit Greenberger-Horne-Zeilinger (GHZ) states or three-qubit W states from many copies of initial partially genuine steerable assemblages of the corresponding states. In each of these cases, we demonstrate that at least one copy of a perfectly genuine steerable assemblage can be distilled with certainty from infinitely many copies of initial assemblages. In case of practical scenarios employing finite copies, we show that the efficiency of our distillation protocols reaches near perfect levels using only a few number of initial assemblages.