Chordal graphs and distinguishability of quantum product states

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...

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Bibliographic Details
Published in:Linear algebra and its applications 2024-08, Vol.694, p.478-498
Main Authors: Kribs, David W., Mintah, Comfort, Nathanson, Michael, Pereira, Rajesh
Format: Article
Language:English
Subjects:
Chordal graphs
Gram matrix
Graph clique cover
Graph parameters
Local operations and classical communication
Operator system
Positive semidefinite matrix
Product states
Quantum state distinguishability
Simplicial vertex
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2024.04.021