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Operational distance and fidelity for quantum channels
 J. Math. Phys
, 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 minim ..."
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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 welldefined for channels between finitedimensional algebras, but it also applies to a certain class of channels between infinitedimensional algebras (explicitly, those channels that possess an operatorvalued 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 CBnorm distance between channels, precisely in the same way as the Bures metric on the density operators associated with statistical states of quantummechanical systems, derived from the wellknown fidelity (‘generalized transition probability’) of Uhlmann, is topologically
ROBUSTNESS PROPERTIES OF A CLASS OF OPTIMAL RISKSENSITIVE CONTROLLERS FOR QUANTUM SYSTEMS 1
"... Abstract: In this note we described the robustness properties of optimal risksensitive controllers for quantum systems. We consider a quantum generalization of risksensitive criteria using the framework of (James, 2004). The robustness properties are derived by evaluating certain RadonNikodym deri ..."
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Abstract: In this note we described the robustness properties of optimal risksensitive controllers for quantum systems. We consider a quantum generalization of risksensitive criteria using the framework of (James, 2004). The robustness properties are derived by evaluating certain RadonNikodym 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 nonclassical feature.
CONTENTS
, 2004
"... 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 minim ..."
Abstract
 Add to MetaCart
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 welldefined for channels between finitedimensional algebras, but it also applies to a certain class of channels between infinitedimensional algebras (explicitly, those channels that possess an operatorvalued 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 CBnorm distance between channels, precisely in the same way as the Bures metric on the density operators associated with statistical states of quantummechanical systems, derived from the wellknown fidelity (‘generalized transition probability’) of Uhlmann, is topologically equivalent to the tracenorm distance. 2000 Mathematics Subject Classification. 46L07, 46L55, 46L60, 47L07.