Tight and attainable quantum speed limit for open systems

TL;DR

This paper introduces a new quantum speed limit for open systems based on a geometric state distance, which is both attainable and tighter than previous bounds, demonstrated through analytical and numerical comparisons.

Contribution

The authors develop a geometric quantum speed limit for open systems that is attainable and tighter than existing bounds, with conditions for geodesic dynamics and validation through examples.

Findings

The new QSL is attainable along geodesic dynamics.

It is tighter than previous quantum speed limits in many cases.

Analytical and numerical comparisons confirm the effectiveness of the new bound.

Abstract

We develop an intuitive geometric picture of quantum states, define a particular state distance, and derive a quantum speed limit (QSL) for open systems. Our QSL is attainable because any initial state can be driven to a final state by the particular dynamics along the geodesic. We present the general condition for dynamics along the geodesic for our QSL. As evidence, we consider the generalized amplitude damping dynamics and the dephasing dynamics to demonstrate the attainability. In addition, we also compare our QSL with others by strict analytic processes as well as numerical illustrations, and show our QSL is tight in many cases. It indicates that our work is significant in tightening the bound of evolution time.