Stochastic Isometries in Quantum Mechanics

Abstract

The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and symmetry transformations. Here a characterization of the isometric stochastic maps is given and possible physical applications are indicated.

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• Ancilla dimension in quantum channel discrimination
• Dissipative Encoding of Quantum Information
• Geometrical and Operational Aspects of Irreversibility