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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 13: Offene Quantensysteme
MP 13.1: Talk
Thursday, March 1, 2012, 09:40–10:05, ZHG 003
Differential Geometry of Coherently Controlled Markovian Open Quantum Systems — •Corey O’Meara1, Gunther Dirr2, and Thomas Schulte-Herbrüggen1 — 1TU-Munich, Dept. Chem. — 2University of Würzburg, Inst. Math.
We extend standard Markovian unital and non-unital quantum channels by allowing for coherent Hamiltonian controls. We show that the geometry of these controlled channels can be described in terms of Lie (sub)semigroups in a way [1] that is more helpful for control engineering than the usual picture of Lindblad and Kossakowski. For standard dissipative interactions with the environment (phase damping, depolarizing, amplitude damping etc) and different coherent controls, we specify the tangent cones (Lie wedges) to the Lie semigroups [2].
These cones are the counterpart of the infinitesimal generator of a single one-parameter semigroup. They comprise all directions the open quantum system can be steered along. Being readily scalable to multi-qubit systems, such a differential characterisation is highly valuable for approximating reachable sets of given initial quantum states in a plethora of experimental implementations. The advantage over estimates by majorisation even increases with system size.
References:
[1] G. Dirr, U. Helmke, I. Kurniawan, and T. Schulte-Herbrüggen, Rep. Math. Phys. 64 (2009) 93–121
[doi:10.1016/S0034-4877(09)90022-2]
[2] C. O’Meara, G. Dirr, and T. Schulte-Herbrüggen, IEEE Trans. Control, in press (2011),
[see: http://arxiv.org/abs/1103.2703v2]