Time scaling and quantum speed limit in non-Hermitian Hamiltonians

We report on a time scaling technique to enhance the performances of quantum protocols in non-Hermitian 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 2 and 3-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 while reducing significantly the damping of the quantum state norm.