Every Little Thing Heat Does Is Magic

TL;DR

This paper introduces thermodynamic witnesses based on energy and heat measurements to certify quantum magic without full state tomography, applicable to various quantum systems.

Contribution

It develops novel energy and heat-based criteria to detect quantum magic, including a nonlinear heat exchange witness, expanding certification methods.

Findings

Energy measurements below the stabilizer ground-state energy indicate nonstabilizerness.

Heat exchange bounds can certify magic even when energy measurements are inconclusive.

The approach detects nonstabilizerness in many-body systems and at quantum critical points.

Abstract

How can one certify that an unknown quantum state possesses magic without resorting to full state tomography? We address this question by introducing two thermodynamic witnesses that rely solely on energy and heat measurements. First, we define the stabilizer ground-state energy as the lowest energy achievable by any stabilizer state, and the stabilizer gap as the separation between this value and the true ground-state energy. Any state whose energy lies below the stabilizer ground-state energy is therefore necessarily nonstabilizer. This leads to a direct witness of magic using only average-energy measurements. To overcome the limitations when direct energy measurements are inconclusive, we further develop a nonlinear witness based on heat exchange with a thermal ancilla. Specifically, we derive fundamental bounds on heat that are satisfied by all stabilizer states; therefore, their violation certifies the presence of magic. We demonstrate the effectiveness of our approach through several examples, ranging from few-body systems where heat exchange reveals nonstabilizerness even when energy measurements alone fail, to the transverse-field Ising chain, where the stabilizer gap becomes maximal at the quantum critical point.