Quantifying magic via quantum $(\alpha,\beta)$ Jensen-Shannon divergence

TL;DR

This paper introduces two novel quantum magic quantifiers based on $( extalpha,eta)$ Jensen-Shannon divergence, offering computational efficiency and insights into magic generation in quantum states.

Contribution

The work proposes new magic quantifiers using quantum $( extalpha,eta)$ divergence, with properties and applications in magic resource theory.

Findings

Quantifiers are efficiently computable in low-dimensional spaces.

Initial nonstabilizerness can enhance magic generation.

Quantifiers provide new tools for magic resource theory.

Abstract

Magic states play an important role in fault-tolerant quantum computation, and so the quantification of magic for quantum states is of great significance. In this work, we propose two new magic quantifiers by introducing two versions of quantum $(\alpha,\beta)$ Jensen-Shannon divergence based on the quantum $(\alpha,\beta)$ entropy and the quantum $(\alpha,\beta)$-relative entropy, respectively. We derive many desirable properties for our magic quantifiers, and find that they are efficiently computable in low-dimensional Hilbert spaces. We also show that the initial nonstabilizerness in the input state can boost the magic generating power for our magic quantifiers with appropriate parameter ranges for a certain class of quantum gates. Our magic quantifiers may provide new tools for addressing some specific problems in magic resource theory.