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.
Highlights
The communication paradigm called local operations and classical communication, usually denoted by its acronym local quantum operations and classical communication (LOCC), is fundamental to quantum information theory, and includes many central topics such as quantum teleportation, data hiding, and many of their derivations [1,2,3]
Our work in the theory of LOCC [10,11,12,13] has for the first time brought techniques and tools from operator theory, operator algebras, and graph theory to the basic theory of quantum state distinguishability in one-way LOCC
The basic set up for the LOCC framework is as follows: multiple parties share a set of quantum states, on which each party can perform local quantum operations
Summary
The communication paradigm called local (quantum) operations and classical communication, usually denoted by its acronym LOCC, is fundamental to quantum information theory, and includes many central topics such as quantum teleportation, data hiding, and many of their derivations [1,2,3]. Given the overlapping nature of some of our results and applications, including improvements on some results as our work progressed, we felt a review paper bringing together a selection of main features from our work could be a useful contribution to the literature. In addition to this exposition, we derive a new graph-theoretic description of one-way distinguishability in an important special case, that of a single-qubit sender.
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