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 finitedimensional algebras, but it also applies to a certain class of channels between infinitedimensional 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

Abstract: In this note we described the robustness properties of optimal risksensitive controllers for quantum systems. We consider a quantum generalization of risk-sensitive criteria using the framework of (James, 2004). The robustness properties are derived by evaluating certain Radon-Nikodym derivatives of the quantum models and of the cost criteria. In addition to induced perturbations in the quantum statistics, perturbations in the cost function are allowed—evidently a non-classical feature.

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 finitedimensional algebras, but it also applies to a certain class of channels between infinitedimensional 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. 2000 Mathematics Subject Classification. 46L07, 46L55, 46L60, 47L07.