Preprint 17/2016

Steering Bell-diagonal states

Quan Quan, Huangjun Zhu, Si-Yuan Liu, Shao-Ming Fei, Heng Fan, and Wen-Li Yang

Contact the author: Please use for correspondence this email.
Submission date: 11. Feb. 2016
Pages: 14
published in: Scientific Reports, 6 (2016), art-no. 22025 
DOI number (of the published article): 10.1038/srep22025
Download full preprint: PDF (6276 kB)

We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality.

02.07.2022, 02:18