Cyclic Einstein-Podolsky-Rosen Steering

TL;DR

This paper introduces a novel cyclic property of tripartite EPR steering in three-qubit states, where each party can steer the next in a cycle, revealing new asymmetries in quantum correlations.

Contribution

It generalizes bipartite one-way EPR steering to a cyclic tripartite scenario, demonstrating a new form of directional quantum steering among three parties.

Findings

Identified a three-qubit state with cyclic steering properties.

Demonstrated that bipartite reduced states are one-way steerable.

Established the directional nature of tripartite EPR steering in a triangular configuration.

Abstract

Einstein-Podolsky-Rosen (EPR) steering is a form of quantum correlation that exhibits a fundamental asymmetry in the properties of quantum systems. Given two observers, Alice and Bob, it is known to exist bipartite entangled states which are one-way steerable in the sense that Alice can steer Bob's state, but Bob cannot steer Alice's state. Here we generalize this phenomenon to three parties and find a cyclic property of tripartite EPR steering. In particular, we identify a three-qubit state whose reduced bipartite states are one-way steerable for arbitrary projective measurements. Moreover, the three-qubit state has a cyclic steering property in the sense, that by arranging the system in a triangular configuration the neighboring parties can steer each others' states only in the same (e.g. clockwise) direction. That is, Alice can steer Bob's state, Bob can steer Charlie's state, and Charlie can steer Alice's state, but not the other way around.