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Zero-error communication via quantum channels, non-commutative graphs and a quantum Lov´asz ϑ function PDF

24 Pages·2011·English
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by ['simone severini']| 2011| 24 pages| English

About Zero-error communication via quantum channels, non-commutative graphs and a quantum Lov´asz ϑ function

This document proposes defining a quantum version of Lovász's θ function to bound the zero-error capacity of quantum channels. It discusses how classical zero-error communication can be formulated using confusability graphs of channels. Lovász's θ function provides an upper bound on the independence number of graphs and the zero-error capacity. The document suggests generalizing these concepts to quantum channels by considering operator spaces as "non-commutative graphs" and defines a quantum θ function as the norm-completion of a naive generalization. It shows this function upper bounds entanglement-assisted zero-error messages and is given by a semidefinite program.

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Author:['simone severini']
Publication Year:2011
Pages:24
Language:English
Format:PDF
Price:FREE
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