The relative entropy of magic and its nonadditivity

TL;DR

This paper analyzes the relative entropy of magic in quantum computing, characterizing single-qubit magic states and proving the nonadditivity of the measure for tensor products.

Contribution

It provides an analytical characterization of single-qubit magic states and demonstrates the nonadditivity of the relative entropy of magic in most cases.

Findings

Magic states and their closest stabilizer states are symmetrically arranged around face centers of the stabilizer octahedron.

The relative entropy of magic is nonadditive for tensor products of single-qubit states in almost all cases.

Analytical results from the relative entropy of entanglement are applied to quantum resource theory.

Abstract

In most stabilizer-based quantum computing schemes, so-called magic states are a necessary resource for implementing non-transversal quantum gates. With the resource theory of magic, it is possible to analyze and quantify the generation of the non-stabilizer states. The relative entropy is a measure used in various resource theories. For single qubits, we characterize magic states and their closest stabilizer states by applying analytical results known from the relative entropy of entanglement and show that the magic states and their closest stabilizer states are arranged symmetrically around the states at the centers of the faces of the stabilizer octahedron. For tensor products of single-qubit states, we prove analytically that the relative entropy of magic is nonadditive in almost all cases.