Quantum speed limit for thermal states

Quantum speed limits are rigorous estimates on how fast a state of a quantum system can depart from the initial state in the course of quantum evolution. Most known quantum speed limits, including the celebrated Mandelstam-Tamm and Margolus-Levitin ones, are general bounds applicable to arbitrary initial states. Here we derive a quantum speed limit for a closed quantum system initially prepared in a thermal state and evolving under a time-dependent Hamiltonian. This quantum speed limit exploits the structure of the thermal state and, in particular, explicitly depends on the temperature. As a consequence, in certain cases it can be dramatically tighter than general quantum speed limits applied to thermal states. The talk is based on arXiv 2009.12538.