Time scaling and quantum speed limit in non-Hermitian Hamiltonians

We report on a time-scaling technique to enhance the performances of quantum control protocols in nonHermitian systems. The considered time scaling involves no extra couplings and yields a significant enhancement of the quantum fidelity for a comparable amount of resources. We discuss the application of this technique to quantum-state transfers in two- and three-level open quantum systems. We derive the quantum speed limit in a system governed by a non-Hermitian Hamiltonian. Interestingly, we show that with an appropriate driving the time-scaling technique preserves the optimality of the quantum speed with respect to the quantum speed limit whereas reducing significantly the damping of the quantum-state norm.