On geometric phases for quantum trajectories
arXiv:quant-ph/0608237 · doi:10.1556/APH.26.2006.1-2.23
Abstract
A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by using Uhlmann's concept of parallel transport along the individual trajectories. We put forward an experimental realization of the geometric phase for a quantum trajectory in interferometry. We argue that the average over the phase factors for all quantum trajectories that build up a given open system evolution, fails to reflect the geometry of the open system evolution itself.
Submitted to the Proceedings of the 13th CEWQO 2006 in Vienna
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