An improved bound for quantum speed limit time in open quantum systems by introducing an alternative fidelity

TL;DR

This paper introduces a new quantum fidelity measure that improves the bounds on quantum speed limit times in open quantum systems, especially for mixed initial states, enhancing our understanding of quantum dynamics.

Contribution

The paper proposes an alternative quantum fidelity satisfying all axioms, leading to a tighter quantum speed limit bound for mixed states in open systems.

Findings

New fidelity satisfies all axioms and is zero for orthogonal states

Derived a sharper quantum speed limit bound for mixed states

Recovers Mandelstamm-Tamm bound for pure states

Abstract

In this paper, we introduce a new alternative quantum fidelity for quantum states which perfectly satisfies all Jozsas axioms and is zero for orthogonal states. By employing this fidelity, we derive an improved bound for quantum speed limit time in open quantum systems in which the initial states can be chosen as either pure or mixed. This bound leads to the well-known Mandelstamm-Tamm type bound for nonunitary dynamics in the case of initial pure states. However, in the case of initial mixed states, the bound provided by the introduced fidelity is tighter and sharper than the obtained bounds in the previous works.