Quantum Coherence Sets The Quantum Speed Limit For Mixed States

We cast observable measure of quantum coherence or asymmetry as a resource to control the quantum speed limit (QSL) for unitary evolutions. For non-unitary evolutions, QSL depends on that of the state of the system and environment together. We show that the product of the time bound and the coherence (asymmetry) or the quantum part of the uncertainty behaves in a geometric way under partial elimination and classical mixing of states. These relations give a new insight to the quantum speed limit. We also show that our bound is experimentally measurable and is tighter than various existing bounds in the literature.