Reachability in InfiniteDimensional Unital Open Quantum Systems with Switchable GKSLindblad Generators
Abstract
In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinitedimensional open quantum dynamical systems following a unital KossakowskiLindblad master equation extended by controls. More precisely, their time evolution shall be governed by an inevitable potentially unbounded Hamiltonian drift term H_{0}, finitely many bounded control Hamiltonians H_{j} allowing for (at least) piecewise constant control amplitudes uj(t)∈&R; plus a bangbang (i.e., onoff) switchable noise term Г_{V} in KossakowskiLindblad form. Generalizing standard majorization results from finite to infinite dimensions, we show that such bilinear quantum control systems allow to approximately reach any target state majorized by the initial one as up to now it only has been known in finite dimensional analogues. The proof of the result is currently limited to the bounded control Hamiltonians H_{j} and for noise terms Г_{V} with compact normal V.
 Publication:

Open Systems and Information Dynamics
 Pub Date:
 2019
 DOI:
 10.1142/S1230161219500148
 arXiv:
 arXiv:1902.03085
 Bibcode:
 2019OSID...2650014V
 Keywords:

 Open quantum systems;
 Kossakowski–Lindblad equation;
 quantum control;
 majorization;
 infinite dimensions;
 Quantum Physics;
 Mathematics  Functional Analysis;
 Mathematics  Optimization and Control
 EPrint:
 29 pages