Operator and Graph Theoretic Techniques for Distinguishing Quantum States via One-Way LOCC

Kribs, David W.; Mintah, Comfort; Nathanson, Michael; Pereira, Rajesh

doi:10.3390/app11209542

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14 October 2021

10 Pages

Operator and Graph Theoretic Techniques for Distinguishing Quantum States via One-Way LOCC

and

Department of Mathematics & Statistics, University of Guelph, Guelph, ON N1G 2W1, Canada

Department of Mathematics, Harvard University, Cambridge, MA 02138, USA

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Appl. Sci.2021, 11(20), 9542;https://doi.org/10.3390/app11209542

This article belongs to the Special Issue Recent Development and Application of Quantum Communication and Security Protocols

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Abstract

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.

Keywords:

quantum communication; quantum states; local operations and classical communication; operator algebras; operator systems; quantum error correction; product states; graph theory

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