Quantum Coherence Sets The Quantum Speed Limit For Mixed States

TL;DR

This paper explores how quantum coherence influences the quantum speed limit (QSL) for mixed states, providing new geometric relations and experimentally measurable bounds that are tighter than previous ones.

Contribution

It introduces a coherence-based resource perspective for QSL, deriving geometric relations and tighter bounds applicable to both unitary and non-unitary evolutions.

Findings

Quantum coherence acts as a resource controlling QSL.

Derived geometric relations under state mixing and elimination.

Proposed bounds are experimentally measurable and tighter than existing bounds.

Abstract

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.