Operational distance and fidelity for quantum channels

Viacheslav P. Belavkin, Giacomo Mauro D'Ariano, Maxim Raginsky

Research output: Contribution to journalArticlepeer-review


We define and study a fidelity criterion for quantum channels, which we term the minimax fidelity, through a noncommutative generalization of maximal Hellinger distance between two positive kernels in classical probability theory. Like other known fidelities for quantum channels, the minimax fidelity is well defined for channels between finite-dimensional algebras, but it also applies to a certain class of channels between infinite-dimensional algebras (explicitly, those channels that possess an operator-valued Radon-Nikodym density with respect to the trace in the sense of Belavkin-Staszewski) and induces a metric on the set of quantum channels that is topologically equivalent to the CB-norm distance between channels, precisely in the same way as the Bures metric on the density operators associated with statistical states of quantum-mechanical systems, derived from the well-known fidelity ("generalized transition probability") of Uhlmann, is topologically equivalent to the trace-norm distance.

Original languageEnglish (US)
Article number062106
JournalJournal of Mathematical Physics
Issue number6
StatePublished - Jun 2005
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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