title: Non-commutativity and local indistinguishability of quantum states.
abstract: We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a complete set of pure orthogonal product states. A constructive distinguishing procedure to obtain the concrete local measurements and classical communications is given. The non-commutativity of ensembles can be also used to characterize the quantumness for classical-quantum or quantum-classical correlated states.
authors.affiliation: School of Mathematical Sciences, Capital Normal University, Beijing 100048, P. R. China.
authors.forename: Teng
authors.initials: T
authors.lastname: Ma
authors.affiliation: Department of Mathematics, School of Science, Beijing Information Science and Technology University, Beijing 100192, P. R. China.
authors.forename: Ming-Jing
authors.initials: MJ
authors.lastname: Zhao
authors.affiliation: 1] Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China [2] College of Mathematics, Tonghua Normal University, Tonghua 134001, P. R. China.
authors.forename: Yao-Kun
authors.initials: YK
authors.lastname: Wang
authors.affiliation: 1] School of Mathematical Sciences, Capital Normal University, Beijing 100048, P. R. China [2] Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany.
authors.forename: Shao-Ming
authors.initials: SM
authors.lastname: Fei