Stabilizer entropies are monotones for magic-state resource theory

TL;DR

This paper proves that stabilizer entropies are valid monotones for magic-state resource theory, extending their applicability to mixed states and providing practical tools for quantifying quantum resources.

Contribution

It establishes the monotonicity of stabilizer entropies for pure states, extends them to mixed states via convex roof, and demonstrates their experimental and computational advantages.

Findings

Stabilizer entropies are monotones for pure states with α ≥ 2.

Linear stabilizer entropies are strong monotones.

Convex roof extension allows efficient evaluation for mixed states.

Abstract

Magic-state resource theory is a powerful tool with applications in quantum error correction, many-body physics, and classical simulation of quantum dynamics. Despite its broad scope, finding tractable resource monotones has been challenging. Stabilizer entropies have recently emerged as promising candidates (being easily computable and experimentally measurable detectors of nonstabilizerness) though their status as true resource monotones has been an open question ever since. In this Letter, we establish the monotonicity of stabilizer entropies for $\alpha \geq 2$ within the context of magic-state resource theory restricted to pure states. Additionally, we show that linear stabilizer entropies serve as strong monotones. Furthermore, we extend stabilizer entropies to mixed states as monotones via convex roof constructions, whose computational evaluation significantly outperforms optimization over stabilizer decompositions for low-rank density matrices. As a direct corollary, we provide improved conversion bounds between resource states, revealing a preferred direction of conversion between magic states. These results conclusively validate the use of stabilizer entropies within magic-state resource theory and establish them as the only known family of monotones that are experimentally measurable and computationally tractable.