On dynamics of quantum states generated by averaging of random shifts

Abstract

Quantum channels are usually studied as the completely positive trace preserving linear mapping of the space of normal quantum states into itself. We study the extension of an above quantum channel to the space of quantum states of general type that are convex combinations of normal states and singular states according to the Yosida–Hewitt decomposition. The interest to the study of quantum dynamics on the set of general quantum states arises in the consideration of a quantum dynamical semigroup acting in a Hilbert space of functions of infinite dimensional argument. In this case the above semigroup maps any pure vector quantum state into a state of general type. This effect can be considered in the example of averaging of quantum dynamical semigroup generated by a shift argument on a random Gaussian vector.