Quantum speed limits for leakage and decoherence

We introduce state-independent, non-perturbative Hamiltonian quantum speed limits for population leakage and fidelity loss, for a gapped open system interacting with a reservoir. These results hold in the presence of initial correlations between the system and the reservoir, under the sole assumption that their interaction and its commutator with the reservoir Hamiltonian are norm-bounded. The reservoir need not be thermal and can be time-dependent. We study the significance of energy mismatch between the system and the local degrees of freedom of the reservoir which directly interact with the system. We demonstrate that, in general, by increasing the system gap we may reduce this energy mismatch, and consequently drive the system and the reservoir into resonance, which can accelerate fidelity loss, irrespective of the thermal properties or state of the reservoir. This implies that quantum error suppression strategies based on increasing the gap are not uniformly beneficial. Our speed limits also yield an elementary lower bound on the relaxation time of spin systems.