title: Steering Bell-diagonal states.
abstract: 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.
authors.affiliation: Institute of Modern Physics, Northwest University, Xi'an 710069, China.
authors.forename: Quan
authors.initials: Q
authors.lastname: Quan
authors.affiliation: Institute for Theoretical Physics, University of Cologne, Cologne 50937, Germany.|Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Huangjun
authors.initials: H
authors.lastname: Zhu
authors.affiliation: Institute of Modern Physics, Northwest University, Xi'an 710069, China.
authors.forename: Si-Yuan
authors.initials: SY
authors.lastname: Liu
authors.affiliation: School of Mathematical Sciences, Capital Normal University, Beijing 100048, China.|Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany.
authors.forename: Shao-Ming
authors.initials: SM
authors.lastname: Fei
authors.affiliation: Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.|Collaborative Innovation Center of Quantum Matter, Beijing 100190, China.|Institute of Modern Physics, Northwest University, Xi'an 710069, China.
authors.forename: Heng
authors.initials: H
authors.lastname: Fan
authors.affiliation: Institute of Modern Physics, Northwest University, Xi'an 710069, China.|Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048, China.
authors.forename: Wen-Li
authors.initials: WL
authors.lastname: Yang