Complexity and capacity bounds for quantum channels

Rupert H. Levene, Vern I. Paulsen, Ivan G. Todorov

Research output: Contribution to journalArticle

8 Citations (Scopus)
146 Downloads (Pure)


We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum channel requires to realise a given operator system as its non-commutative confusability graph. We describe quantum complexity as a generalised minimum semidefinite rank and, in the case of a graph operator system, as a quantum intersection number. The quantum complexity and a closely related quantum version of orthogonal rank turn out to be upper bounds for the Shannon zero-error capacity of a quantum channel, and we construct examples for which these bounds beat the best previously known general upper bound for the capacity of quantum channels, given by the quantum Lovasz theta number
Original languageEnglish
Article number8355678
Pages (from-to)6917-6928
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number10
Early online date07 May 2018
Publication statusPublished - 01 Oct 2018

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