Mutual Mana: Converting Local Magic into Correlations via Discrete Beamsplitters

TL;DR

This paper introduces mutual mana, a measure of magic correlations in quantum systems, demonstrating how discrete beamsplitters can convert local magic into shared magic correlations, with explicit formulas and comparisons to other correlation measures.

Contribution

It defines mutual mana as a new measure of magic correlations and analyzes their generation and properties via discrete beamsplitters in multipartite quantum systems.

Findings

Mutual mana quantifies magic correlations analogous to quantum mutual information.

Discrete beamsplitters can fully convert local magic into shared magic correlations.

Explicit formulas for mutual mana are derived for several qutrit states.

Abstract

Magic (non-stabilizerness) is a key resource for achieving universal fault-tolerant quantum computation beyond classical computation. While previous studies have primarily focused on magic in single systems, its interactions and distribution in multipartite settings remain largely unexplored. In this work, we introduce mutual mana as a measure of magic correlations defined in close analogy with quantum mutual information. Our definition builds upon mana, which is the established quantifier of magic based on discrete Wigner function negativity. We characterize magic correlations generated by discrete beamsplitters, whose Gaussian counterparts are fundamental components in quantum optics and quantum technologies. We show that coupling a magic state with a stabilizer vacuum state via a discrete beamsplitter will induce a full conversion of local magic into mutual mana, thereby establishing a mechanism for redistributing magic resources as magic correlations. We reveal the fundamental properties of mutual mana and derive its explicit expressions for several prototypical qutrit states subject to a discrete beamsplitter. We make a comparative study of mutual mana with several established quantifiers of correlations generated by the qutrit beamsplitter, including quantum mutual information, mutual $L^1$-norm magic, and mutual stabilizer 2-R\'enyi entropy.