dorsal/arxiv
View SchemaOperational distance and fidelity for quantum channels
| Authors | Viacheslav P. Belavkin, Giacomo Mauro D'Ariano, Maxim Raginsky |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408159 |
| URL | https://arxiv.org/abs/quant-ph/0408159 |
| DOI | 10.1063/1.1904510 |
| Journal | J. Math. Phys. 46 062106 (2005) |
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.
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"abstract": "We define and study a fidelity criterion for quantum channels, which we term\nthe minimax fidelity, through a noncommutative generalization of maximal\nHellinger distance between two positive kernels in classical probability\ntheory. Like other known fidelities for quantum channels, the minimax fidelity\nis well-defined for channels between finite-dimensional algebras, but it also\napplies to a certain class of channels between infinite-dimensional algebras\n(explicitly, those channels that possess an operator-valued Radon--Nikodym\ndensity with respect to the trace in the sense of Belavkin--Staszewski) and\ninduces a metric on the set of quantum channels which is topologically\nequivalent to the CB-norm distance between channels, precisely in the same way\nas the Bures metric on the density operators associated with statistical states\nof quantum-mechanical systems, derived from the well-known fidelity\n(`generalized transition probability\u0027) of Uhlmann, is topologically equivalent\nto the trace-norm distance.",
"arxiv_id": "quant-ph/0408159",
"authors": [
"Viacheslav P. Belavkin",
"Giacomo Mauro D\u0027Ariano",
"Maxim Raginsky"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"math.OA"
],
"doi": "10.1063/1.1904510",
"journal_ref": "J. Math. Phys. 46 062106 (2005)",
"title": "Operational distance and fidelity for quantum channels",
"url": "https://arxiv.org/abs/quant-ph/0408159"
},
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