Operational distance and fidelity for quantum channels
- 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, Vol. 46, Issue 6; Other Information: DOI: 10.1063/1.1904510; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Distance between quantum states in the presence of initial qubit-environment correlations: A comparative study
Monotonic multi-state quantum f-divergences