Stuttgart 2012 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 35: Poster 2
Q 35.31: Poster
Wednesday, March 14, 2012, 16:30–19:00, Poster.I+II
Introduction to the Lie-Semigroup Picture of Markovian Open Quantum Systems — •Corey O’Meara1, Gunther Dirr2, and Thomas Schulte-Herbrüggen1 — 1TU-Munich, Dept. Chem. — 2University of Würzburg, Inst. Math.
In practical quantum control, a fundamental question is into which states can one coherently steer a given initial state subject to relaxation.
Before determining such reachable sets for coherently controlled channels, we step back and analyse the set of all directions along which a given dissipative system can be steered coherently. To this end, we build on the established fact that Markovian quantum channels form Lie (sub)semigroups [1]. So here we analyse their tangent cones. Such cones (Lie wedges) are key to understanding the dynamics of controlled unital and non-unital channels. They can be parametrized and constructed explicitly for many types of qubit and multi-qubit systems [2].
Finally, the cones provide valuable tools to approximate reachable sets, where the advantage over current estimates 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]