title: Beyond Gisin's Theorem and its Applications: Violation of Local Realism by Two-Party Einstein-Podolsky-Rosen Steering.
abstract: We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin's theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications.
authors.affiliation: 1] Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China [2] Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543.
authors.forename: Jing-Ling
authors.initials: JL
authors.lastname: Chen
authors.affiliation: 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: Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China.
authors.forename: Zhen-Peng
authors.initials: ZP
authors.lastname: Xu
authors.affiliation: 1] Key Laboratory of Quantum Information, University of Science and Technology of China, 230026 Hefei, People's Republic of China [2] Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China.
authors.forename: Yu-Chun
authors.initials: YC
authors.lastname: Wu
authors.affiliation: Pillar of Engineering Product Development, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372.
authors.forename: Chunfeng
authors.initials: C
authors.lastname: Wu
authors.affiliation: 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] Institute of Theoretical Physics and Astrophysics, University of Gdańsk, PL-80-952 Gdańsk, Poland [2] Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, 230026 Hefei, China.
authors.forename: Marek
authors.initials: M
authors.lastname: Żukowski
authors.affiliation: 1] Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 [2] National Institute of Education,1 Nanyang Walk, Singapore 637616 [3] Institute of Advanced Studies, Nanyang Technological University, 60 Nanyang View, Singapore 639673.
authors.forename: L C
authors.initials: LC
authors.lastname: Kwek