Cyclic Einstein-Podolsky-Rosen Steering

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.

11 pages, 2 figures, 1 table

References in corpus (11)

• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Observation of one-way Einstein-Podolsky-Rosen steering
• Taming multiparticle entanglement
• Grothendieck's constant and local models for noisy entangled quantum states
• Einstein-Podolsky-Rosen steering and the steering ellipsoid
• Quantum steering ellipsoids, extremal physical states and monogamy
• EPR entanglement strategies in two-well BEC
• Qutrit witness from the Grothendieck constant of order four
• Persistency of entanglement and nonlocality in multipartite quantum systems