A magic monotone for faithful detection of non-stabilizerness in mixed states

TL;DR

This paper presents a new monotone for detecting non-stabilizerness in quantum states, applicable to both pure and mixed states, based on stabilizer polytope boundaries, offering a more efficient computational method.

Contribution

A novel monotone and witness for quantifying and detecting magic in quantum states, improving computational efficiency over existing measures.

Findings

Provides necessary and sufficient criteria for magic detection.

Uses hyperplane inequalities to characterize stabilizer polytope boundaries.

More computationally efficient than robustness of magic.

Abstract

We introduce a monotone to quantify the amount of non-stabilizerness (or magic for short), in an arbitrary quantum state. The monotone gives a necessary and sufficient criterion for detecting the presence of magic for both pure and mixed states. The monotone is based on determining the boundaries of the stabilizer polytope in the space of Pauli string expectation values. The boundaries can be described by a set of hyperplane inequations, where violation of any one of these gives a necessary and sufficient condition for magic. The monotone is constructed by finding the hyperplane with the maximum violation and is a type of Minkowski functional. We also introduce a witness based on similar methods. The approach is more computationally efficient than existing faithful mixed state monotones such as robustness of magic due to the smaller number and discrete nature of the parameters to be optimized.