Reachability in Infinite-Dimensional Unital Open Quantum Systems with Switchable GKS-Lindblad Generators

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 infinite-dimensional open quantum dynamical systems following a unital Kossakowski-Lindblad master equation extended by controls. More precisely, their time evolution shall be governed by an inevitable potentially unbounded Hamiltonian drift term H₀, finitely many bounded control Hamiltonians H_j allowing for (at least) piecewise constant control amplitudes uj(t)∈&R; plus a bang-bang (i.e., on-off) switchable noise term Г_V in Kossakowski-Lindblad 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.