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 H_0, finitely many bounded control Hamiltonians H_j allowing for (at least) piecewise constant control amplitudes u_j(t)∈ℝ plus a bang-bang (i.e. on-off) switchable noise term Γ_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 only has been known in finite dimensional analogues.—The proof of the result is currently limited to the control Hamiltonians H_j being bounded and noise terms Γ_V with compact normal V.