Quantum coherence sets the quantum speed limit for mixed states

• QSL for any general processes is proposed.
• Quantum coherence (asymmetry) is portrayed as a resource for QSL.
• A tighter quantum speed limit is proposed.
• QSL under mixing and partial elimination of states is studied.

We cast observable measure of quantum coherence 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 into the quantum speed limit. We also show that our bound is experimentally measurable and is tighter than various existing bounds in the literature.