title: Multipartite quantum correlations and local recoverability.
abstract: Characterizing genuine multipartite quantum correlations in quantum physical systems has historically been a challenging problem in quantum information theory. More recently, however, thetotal correlationormultipartite informationmeasure has been helpful in accomplishing this goal, especially with the multipartite symmetric quantum (MSQ) discord (Pianiet al.2008Phys. Rev. Lett.100, 090502. (doi:10.1103/PhysRevLett.100.090502)) and the conditional entanglement of multipartite information (CEMI) (Yanget al.2008Phys. Rev. Lett.101, 140501. (doi:10.1103/PhysRevLett.101.140501)). Here, we apply a recent and significant improvement of strong subadditivity of quantum entropy (Fawzi & Renner 2014 (http://arxiv.org/abs/1410.0664)) in order to develop these quantities further. In particular, we prove that the MSQ discord is nearly equal to zero if and only if the multipartite state for which it is evaluated is approximately locally recoverable after performing measurements on each of its systems. Furthermore, we prove that the CEMI is a faithful entanglement measure, i.e. it vanishes if and only if the multipartite state for which it is evaluated is a fully separable state. Along the way, we provide an operational interpretation of the MSQ discord in terms of the partial state distribution protocol, which in turn, as a special case, gives an interpretation for the original discord quantity. Finally, we prove an inequality that could potentially improve upon the Fawzi-Renner inequality in the multipartite context, but it remains an open question to determine whether this is so.
authors.affiliation: Hearne Institute for Theoretical Physics, Center for Computation and Technology , Department of Physics and Astronomy, Louisiana State University , Baton Rouge, LA 70803, USA.
authors.forename: Mark M
authors.identifier: 0000-0002-3916-4462
authors.initials: MM
authors.lastname: Wilde
keywords: conditional entanglement of multipartite information; conditional quantum mutual information; multipartite quantum correlation; multipartite symmetric quantum discord; quantum Markov chains