Decoherence and Noise in Loschmidt Echo Experiments

Abstract

We discuss some recent results concerning the decoherence in controlled quantum open systems within the mathematical setting corresponding to motion reversal experiments (the Loschmidt echo). We compare the case of randomly chosen sequence of unitary dynamical maps with the case of a constant dynamics corresponding to a classically chaotic evolution. The interplay between chaos and decoherence is illustrated by the new numerical results on the quantum Arnold cat map perturbed by a measurement process. Open problems related to the simple operational characterization of the decoherence strength are discussed.

Linear dynamical entropy and free-independence for quantized linear maps on the torus

“…fits quite well with the values of A close to 1. The exponential decay can be explained assuming that the quantum variables F (m, j) = U m P j , m = 0 behave like independent random variables in the standard sense (11) with the mean value…”

“…Here N is the dimension of the "effective" Hilbert space consisting of physically admissible states under certain given conditions. It is interesting that as the "entropy" we can put quite different quantities: 1) von Neumann entropy of the initially pure state [5], 2) Shannon entropy computed for diagonal elements in a fixed orthonormal basis [6], 3) Coherent states Shannon entropy [7], 4) Quantum dynamical entropy expressed in terms of multitime correlation matrices [1], 6) The quantities of above with the Shannon (von Neumann) entropy replaced by the Renyi αentropies [8,9,10,11]. It is also clear that the entropy production rate (EnPR) given by h KS can be observed only in a certain regime.…”

“…In the last decade the relations between ergodic properties of classical systems and the dynamical phenomena for the corresponding quantized systems were discussed in a number of papers. In particular the sensitivity of the time evolution of quantum open systems with respect to external perturbations has been studied in terms of entropic quantities, purity of the state or fidelity in the spin-echo settings [1][2][3][4][5][6][7][8][9][10][11]. In most cases the external perturbation is modelled by the irreversible quantum dynamics combined with a unitary (Hamiltonian ) self-dynamics of the system.…”

“…(5) the quantities of above with the Shannon (von Neumann) entropy replaced by the Renyi α-entropies [8][9][10][11].…”