Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions

TL;DR

This paper uses information geometry to analyze quantum driving schemes, focusing on the complexity and efficiency of entropy production during state transfer, and identifies trade-offs between speed, efficiency, and complexity.

Contribution

It introduces a geometric framework for evaluating quantum control paths based on entropy production, complexity, and efficiency, providing a new measure and analytical estimates.

Findings

Higher entropic speed correlates with lower efficiency.

Optimal paths are geodesics minimizing entropy production.

The framework ranks different quantum driving schemes based on complexity and efficiency.

Abstract

We present an information geometric characterization of quantum driving schemes specified by su(2;C) time-dependent Hamiltonians in terms of both complexity and efficiency concepts. By employing a minimum action principle, the optimum path connecting initial and final states on the manifold in finite-time is the geodesic path between the two states. In particular, the total entropy production that occurs during the transfer is minimized along these optimum paths. For each optimum path that emerges from the given quantum driving scheme, we evaluate the so-called information geometric complexity (IGC) and our newly proposed measure of entropic efficiency constructed in terms of the constant entropy production rates that specify the entropy minimizing paths being compared. From our analytical estimates of complexity and efficiency, we provide a relative ranking among the driving schemes being investigated. Finally, we conclude by commenting on the fact that an higher entropic speed in quantum transfer processes seems to necessarily go along with a lower entropic efficiency together with a higher information geometric complexity.