Action quantum speed limits

TL;DR

This paper introduces action quantum speed limits (QSLs) that depend on the traversal speed along a path, providing bounds on the minimal time to connect quantum states, with implications for optimal control and interpretation of QSLs.

Contribution

The paper proposes a new family of QSLs based on action and instantaneous speed, contrasting with traditional geometric bounds, and analyzes their interpretation in open quantum systems.

Findings

Action QSLs depend on traversal speed and path

Optimal control techniques demonstrate consistency of bounds

QSLs indicate optimality relative to geodesic paths

Abstract

We introduce action quantum speed limits (QSLs) as a family of bounds on the minimal time to connect two states that, unlike the usual geometric approach, crucially depend on how the path is traversed, i.e. on the instantaneous speed. The two approaches provide consistent bounds when the instantaneous speed is optimized along a fixed path and we demonstrate this explicitly for the case of a thermalizing qubit employing techniques from optimal control theory. In addition, we critically analyze the interpretation of QSLs based on different choices of metric establishing that, in general, these open system QSL times provide an indication of optimality with respect to the geodesic path, rather than necessarily being indicative of an achievable minimal time.