Critical behaviors of non-stabilizerness in quantum spin chains

• URL: http://arxiv.org/abs/2309.00676v3
• Date: Sun, 14 Jul 2024 12:10:25 GMT
• Title: Critical behaviors of non-stabilizerness in quantum spin chains
• Authors: Poetri Sonya Tarabunga,
• Abstract summary: Non-stabilizerness measures the extent to which a quantum state deviates from stabilizer states. In this work, we investigate the behavior of non-stabilizerness around criticality in quantum spin chains.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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