Operational distance and fidelity for quantum channels

Journal Article · Wed Jun 01 04:00:00 EDT 2005 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.1904510· OSTI ID:20699191

Belavkin, Viacheslav P; D'Ariano, Giacomo Mauro; Raginsky, Maxim ^[1]

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1. Department of Mathematics, University of Nottingham, NG7 2RD Nottingham (United Kingdom)

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.

• OSTI ID: 20699191
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 6 Vol. 46; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
COMMUTATION RELATIONS
DENSITY
DISTANCE
HILBERT SPACE
PROBABILITY
QUANTUM MECHANICS
TOPOLOGY