Karlsruhe 2011 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 21: Quantum Information III
MP 21.2: Talk
Thursday, March 31, 2011, 15:15–15:35, 30.45: 201
Geometry of Markovian Quantum Channels Seen as Lie Semigroups — •Corey O'Meara1, Gunther Dirr2, and Thomas Schulte-Herbrüggen1 — 1Dept. Chem. TU-Munich, Germany — 2Math. Inst., University of Würzburg, Germany
A plethora of Markovian quantum channels under various degrees of Hamiltonian control are analysed in terms of their differential geometric properties. To this end, the set of all Markovian CP maps described as the solutions of a controlled Kossakowski-Lindblad master equation are characterized as Lie (sub)semigroups. Thus, for depolarising, dephasing, amplitude damping, bit-flip, or phase-flip channels we focus on the specific structure of their Lie wedges being suitable tangent cones encapsulating the control directions as their edge.
Since the geometry of the Lie wedge completely determines the time evolution underlying the controlled quantum channel, this most illustrative insight may subsequently be exploited to approximate the reachable sets of given initial quantum states. Finally, possible applications are outlined.