Sharing quantum steering among multiple Alices and Bobs via a two-qubit Werner state

TL;DR

This paper investigates how quantum steering can be shared among multiple Alices and Bobs using a two-qubit Werner state, revealing new sharing limits and robustness conditions for quantum correlations.

Contribution

It introduces a sequential steering sharing scenario with multiple Alices and Bobs on a Werner state, revealing new sharing limits and robustness conditions.

Findings

Maximum Alices sharing steering with one Bob increases from 2 to 5 as measurement settings increase from 2 to 16.

At most 2 Alices can share steering with 2 Bobs for fixed measurement settings, but 4 or more can share with a single Bob.

Required Werner state purity varies from 0.503 to 0.979 for sharing robustness.

Abstract

Quantum steering, a type of quantum correlation with unique asymmetry, has important applications in asymmetric quantum information tasks. We consider a new quantum steering scenario in which one half of a two-qubit Werner state is sequentially measured by multiple Alices and the other half by multiple Bobs. We find that the maximum number of Alices who can share steering with a single Bob increases from 2 to 5 when the number of measurement settings $N$ increases from 2 to 16. Furthermore, we find a counterintuitive phenomenon that for a fixed $N$, at most 2 Alices can share steering with 2 Bobs, while 4 or more Alices are allowed to share steering with a single Bob. We further analyze the robustness of the steering sharing by calculating the required purity of the initial Werner state, the lower bound of which varies from 0.503(1) to 0.979(5). Finally, we show that our both-sides sequential steering sharing scheme can be applied to control the steering ability, even the steering direction, if an initial asymmetric state or asymmetric measurement is adopted. Our work gives insights into the diversity of steering sharing and can be extended to study the problems such as genuine multipartite quantum steering when the sequential unsharp measurement is applied.