Purity Speed Limit of Open Quantum Systems from Magic Subspaces

TL;DR

This paper introduces Magic Subspaces to determine the maximum and minimum rates of purity change in dissipative quantum systems, establishing a tight purity speed limit based on relaxation rates, with explicit examples for two- and three-level systems.

Contribution

It defines Magic Subspaces for controlling purity dynamics in open quantum systems and derives a new, tight purity speed limit dependent only on relaxation rates.

Findings

Magic Subspaces characterize extremal purity change rates.

The derived speed limit outperforms existing bounds.

Explicit examples demonstrate the limit's tightness for two- and three-level systems.

Abstract

We introduce the concept of Magic Subspaces for the control of dissipative N- level quantum systems whose dynamics are governed by Lindblad equation. For a given purity, these subspaces can be defined as the set of density matrices for which the rate of purity change is maximum or minimum. Adding fictitious control fields to the system so that two density operators with the same purity can be connected in a very short time, we show that magic subspaces allow to derive a purity speed limit, which only depends on the relaxation rates. We emphasize the superiority of this limit with respect to established bounds and its tightness in the case of a two-level dissipative quantum system. The link between the speed limit and the corresponding time-optimal solution is discussed in the framework of this study. Explicit examples are described for two- and three- level quantum systems.