title: Test of Einstein-Podolsky-Rosen steering based on the all-versus-nothing proof.
abstract: In comparison with entanglement and Bell nonlocality, Einstein-Podolsky-Rosen steering is a newly emerged research topic and in its incipient stage. Although Einstein-Podolsky-Rosen steering has been explored via violations of steering inequalities both theoretically and experimentally, the known inequalities in the literatures are far from well-developed. As a result, it is not yet possible to observe Einstein-Podolsky-Rosen steering for some steerable mixed states. Recently, a simple approach was presented to identify Einstein-Podolsky-Rosen steering based on all-versus-nothing argument, offering a strong condition to witness the steerability of a family of two-qubit (pure or mixed) entangled states. In this work, we show that the all-versus-nothing proof of Einstein-Podolsky-Rosen steering can be tested by measuring the projective probabilities. Through the bound of probabilities imposed by local-hidden-state model, the proposed test shows that steering can be detected by the all-versus-nothing argument experimentally even in the presence of imprecision and errors. Our test can be implemented in many physical systems and we discuss the possible realizations of our scheme with non-Abelian anyons and trapped ions.
authors.affiliation: 1] Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 [2] Pillar of Engineering Product Development, Singapore University of Technology and Design, 20 Dover Drive, Singapore 138682.
authors.forename: Chunfeng
authors.initials: C
authors.lastname: Wu
authors.affiliation: 1] Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 [2] Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China.
authors.forename: Jing-Ling
authors.initials: JL
authors.lastname: Chen
authors.affiliation: 1] Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 [2] Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China.
authors.forename: Xiang-Jun
authors.initials: XJ
authors.lastname: Ye
authors.affiliation: 1] Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 [2] Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China.
authors.forename: Hong-Yi
authors.initials: HY
authors.lastname: Su
authors.affiliation: Department of Physics and Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors.forename: Dong-Ling
authors.initials: DL
authors.lastname: Deng
authors.affiliation: Microsoft Research, Station Q, University of California, Santa Barbara, CA 93106, USA.
authors.forename: Zhenghan
authors.initials: Z
authors.lastname: Wang
authors.affiliation: 1] Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 [2] Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117551.
authors.forename: C H
authors.initials: CH
authors.lastname: Oh