Critical behaviors of non-stabilizerness in quantum spin chains

TL;DR

This paper explores how non-stabilizerness, a resource for quantum computation, behaves near critical points in quantum spin chains, revealing universal scaling properties similar to entanglement.

Contribution

It introduces Rényei generalizations of mana to quantify non-stabilizerness in large systems and demonstrates universal logarithmic scaling in critical quantum models.

Findings

Mutual mana exhibits universal logarithmic scaling with distance.

Rényei generalizations effectively quantify non-stabilizerness in large systems.

Non-stabilizerness shows critical behavior similar to entanglement in conformal field theory.

Abstract

Non-stabilizerness - commonly known as magic - measures the extent to which a quantum state deviates from stabilizer states and is a fundamental resource for achieving universal quantum computation. In this work, we investigate the behavior of non-stabilizerness around criticality in quantum spin chains. To quantify non-stabilizerness, we employ a monotone called mana, based on the negativity of the discrete Wigner function. This measure captures non-stabilizerness for both pure and mixed states. We introduce R\'enyi generalizations of mana, which are also measures of non-stabilizerness for pure states, and utilize it to compute mana in large quantum systems. We consider the three-state Potts model and its non-integrable extension and we provide strong evidence that the mutual mana exhibits universal logarithmic scaling with distance in conformal field theory, as is the case for entanglement.