A strong converse for the quantum state merging protocol

Abstract: The Polyanskiy-Verd\'{u} paradigm provides an elegant way of using generalized-divergences to obtain strong converses and thus far has remained confined to protocols involving channels (classical or quantum). In this paper, drawing inspirations from it, we provide strong converses for protocols involving LOCC (local operations and classical communication). The key quantity that we work with is the R\'{e}nyi relative entropy of entanglement. We provide a strong converse for the quantum state merging protocol that gives an exponential decay of the fidelity of the protocol for rates below the optimum with the number of copies of the state and are provided both for entanglement rate with LOCC as well as for classical communication with one-way LOCC. As an aside, the developments also yield short strong converses for the entanglement-concentration of pure states and the Schumacher compression.