title: Entanglement and Coherence in Quantum State Merging.
abstract: Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging, where two parties aim to merge their tripartite quantum state parts. In standard quantum state merging, entanglement is considered to be an expensive resource, while local quantum operations can be performed at no additional cost. However, recent developments show that some local operations could be more expensive than others: it is reasonable to distinguish between local incoherent operations and local operations which can create coherence. This idea leads us to the task of incoherent quantum state merging, where one of the parties has free access to local incoherent operations only. In this case the resources of the process are quantified by pairs of entanglement and coherence. Here, we develop tools for studying this process and apply them to several relevant scenarios. While quantum state merging can lead to a gain of entanglement, our results imply that no merging procedure can gain entanglement and coherence at the same time. We also provide a general lower bound on the entanglement-coherence sum and show that the bound is tight for all pure states. Our results also lead to an incoherent version of Schumacher compression: in this case the compression rate is equal to the von Neumann entropy of the diagonal elements of the corresponding quantum state.
authors.affiliation: ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain.|Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, D-14195 Berlin, Germany.
authors.forename: A
authors.initials: A
authors.lastname: Streltsov
authors.affiliation: Department of Physics and Astronomy, Southern Illinois University, Carbondale, Illinois 62901, USA.
authors.forename: E
authors.initials: E
authors.lastname: Chitambar
authors.affiliation: ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain.
authors.forename: S
authors.initials: S
authors.lastname: Rana
authors.affiliation: ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain.
authors.forename: M N
authors.initials: MN
authors.lastname: Bera
authors.affiliation: Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain.|ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, ES-08010 Barcelona, Spain.
authors.forename: A
authors.initials: A
authors.lastname: Winter
authors.affiliation: ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain.|ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, ES-08010 Barcelona, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Lewenstein