Critical behaviors of non-stabilizerness in quantum spin chains

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 Rényi 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 quantum Potts model and its non-integrable extension and we provide numerical evidence that the mutual mana exhibits universal logarithmic scaling with distance in conformal field theory, as is the case for entanglement. Comparing this with the scaling in gapped phases, we demonstrate that the scaling of mutual mana serves as a valuable tool for distinguishing between critical and non-critical behavior.