title: Universal Steering Criteria.
abstract: We propose a general framework for constructing universal steering criteria that are applicable to arbitrary bipartite states and measurement settings of the steering party. The same framework is also useful for studying the joint measurement problem. Based on the data-processing inequality for an extended Rényi relative entropy, we then introduce a family of steering inequalities, which detect steering much more efficiently than those inequalities known before. As illustrations, we show unbounded violation of a steering inequality for assemblages constructed from mutually unbiased bases and establish an interesting connection between maximally steerable assemblages and complete sets of mutually unbiased bases. We also provide a single steering inequality that can detect all bipartite pure states of full Schmidt rank. In the course of study, we generalize a number of results intimately connected to data-processing inequalities, which are of independent interest.
authors.affiliation: Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.|Institute for Theoretical Physics, University of Cologne, Cologne 50937, Germany.
authors.forename: Huangjun
authors.initials: H
authors.lastname: Zhu
authors.affiliation: Graduate School of Mathematics, Nagoya University, Nagoya 464-0814, Japan.|Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore.
authors.forename: Masahito
authors.initials: M
authors.lastname: Hayashi
authors.affiliation: School of Mathematics and Systems Science, Beihang University, Beijing 100191, China.|International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China.
authors.forename: Lin
authors.initials: L
authors.lastname: Chen