Quantum operation time reversal
Abstract
The dynamics of an open quantum system can be described by a quantum operation: A linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to the time reversal of a classical Markov transition matrix. Since open quantum dynamics are stochastic, and not, in general, deterministic, the time reversal is not, in general, an inversion of the dynamics. Rather, the system relaxes toward equilibrium in both the forward and reverse time directions. The probability of a quantum trajectory and the conjugate, time reversed trajectory are related by the heat exchanged with the environment.
 Publication:

Physical Review A
 Pub Date:
 March 2008
 DOI:
 10.1103/PhysRevA.77.034101
 arXiv:
 arXiv:0706.3749
 Bibcode:
 2008PhRvA..77c4101C
 Keywords:

 05.30.Ch;
 05.70.Ln;
 Quantum ensemble theory;
 Nonequilibrium and irreversible thermodynamics;
 Quantum Physics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 4 pages