Operator and Graph-Theoretic Techniques for Distinguishing Quantum States in the Local Operations and Classical Communication Framework

正樹 尾張

David W. Kribs, Comfort Mintah, Michael Nathanson +1 more

We bring together in one place some of the main results and applications from our recent work on quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time to investigate the topic of distinguishability of sets of quantum states in quantum communication, with particular reference to the framework of one-way local quantum operations and classical communication (LOCC). We also derive a new graph-theoretic description of distinguishability in the case of a single-qubit sender.

Benjamin W. Schumacher, Michael D. Westmoreland

Comfort Mintah, David W. Kribs, Michael Nathanson +1 more

We investigate a graph-theoretic approach to the problem of distinguishing quantum product states in the fundamental quantum communication framework called local operations and classical communication (LOCC). We identify chordality as the key graph structure that drives distinguishability in one-way LOCC, and we derive a one-way LOCC characterization for chordal graphs that establishes a connection with the theory of matrix completions. We also derive minimality conditions on graph parameters that allow for the determination of indistinguishability of states. We present a number of applications and examples built on these results.

David W. Kribs, Comfort Mintah, Michael Nathanson +1 more

We investigate a graph-theoretic approach to the problem of distinguishing quantum product states in the fundamental quantum communication framework called local operations and classical communication (LOCC). We identify chordality as the key graph structure that drives distinguishability in one-way LOCC, and we derive a one-way LOCC characterization for chordal graphs that establishes a connection with the theory of matrix completions. We also derive minimality conditions on graph parameters that allow for the determination of indistinguishability of states. We present a number of applications and examples built on these results.

Sooyeong Kim, David W. Kribs, Michael Nathanson +2 more

We consider the problem of distinguishing sets of quantum product states with local operations and classical communication (LOCC). Recent work has used graph theory to identify sets of product states distinguishable with one-way LOCC. We extend these efforts to full two-way LOCC, with the first significant analysis of the set of graphs corresponding to bipartite product states that can be distinguished with two-way protocols after finitely many steps. We derive basic closure properties of the set of distinguishable graphs and identify some classes of graphs that guarantee local distinguishability and some graphs that do not. We also include several examples and forward-looking comments.