Clifford Ergotropy

TL;DR

This paper introduces Clifford ergotropy, a measure of extractable energy under Clifford operations, and explores its bounds, implications for quantum systems, and connections to thermodynamics and magic resources.

Contribution

It defines Clifford ergotropy, establishes universal bounds related to magic, and analyzes its behavior in simple and many-body quantum systems.

Findings

Bounds on Clifford ergotropy decrease with increasing magic.

Notable transition observed in the control landscape of Clifford ergotropy for two-qubit systems.

Implications for a form of the second law of thermodynamics under Clifford operations.

Abstract

We discuss the interplay between thermodynamics and magic resources in closed quantum dynamics by introducing Clifford ergotropy, the amount of extractable energy under the restriction to Clifford operations. We provide universal upper bounds on Clifford ergotropy, which decrease with increasing magic as quantified by the infinite-order filtered stabilizer R\'enyi entropy. We demonstrate the utility of this bound for one- and two-qubit systems, with the latter exhibiting a notable transition in the control landscape of Clifford ergotropy. Finally, we show that our analysis has nontrivial consequences even for many-body systems where the exact optimization is generally difficult to perform, including a form of the second law of thermodynamics under Clifford operations for typical quantum states.