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Operational distance and fidelity for quantum channels | | Viacheslav P. Belavkin
; Giacomo Mauro D’Ariano
; Maxim Raginsky
; | | Date: |
26 Aug 2004 | | Subject: | Quantum Physics; Mathematical Physics; Operator Algebras | quant-ph math-ph math.MP math.OA | | Abstract: | 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 which 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. | | Source: | arXiv, quant-ph/0408159 | | Services: | Forum | Review | PDF | Favorites | |
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