Vector Representations of Graphs and Distinguishing Quantum Product States with One-way LOCC
arXiv:1912.10483 · doi:10.1016/j.laa.2020.05.017
Abstract
Distinguishing sets of quantum states shared by two parties using only local operations and classical communication measurements is a fundamental topic in quantum communication and quantum information theory. We introduce a graph-theoretic approach, based on the theory of vector representations of graphs, to the core problem of distinguishing product states with one-way LOCC. We establish a number of results that show how distinguishing such states can be framed in terms of properties of the underlying graphs associated with a set of vector product states. We also present a number of illustrative examples.
Most recent version includes a fix of condition 3 of Theorem 1, and removal of related peripheral results Corollary 1, 2, and 3