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  • Letter
  • Open Access

Breaking global symmetries with locality-preserving operations

Michele Mazzoni1,*, Luca Capizzi2, and Lorenzo Piroli1

  • *Contact author: Michele.mazzoni7@unibo.it
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Phys. Rev. Research 8, L012056 – Published 6 March, 2026

DOI: https://doi.org/10.1103/gcjj-88j6

Abstract

In the general framework of quantum resource theories, one typically only distinguishes between operations that can or cannot generate the resource of interest. In many-body settings, one can further characterize quantum operations based on underlying geometrical constraints, and a natural question is to understand the power of resource-generating operations that preserve locality. In this work, we address this question within the resource theory of asymmetry, which has recently found applications in the study of many-body symmetry-breaking and symmetry-restoration phenomena. We consider symmetries corresponding to both Abelian and non-Abelian compact groups with a homogeneous action on the space of N qubits, focusing on the prototypical examples of U(1) and SU(2). We study the so-called G asymmetry ΔSNG, and present two main results. First, we derive a general bound on the asymmetry that can be generated by locality-preserving operations acting on product states. We prove that, in any spatial dimension, ΔSNG≤(1/2)ΔSNG,max[1+o(1)], where ΔSNG,max is the maximum value of the G asymmetry in the full many-body Hilbert space. Second, we show that locality-preserving operations can generate maximal asymmetry, ΔSNG∼ΔSNG,max, when applied to symmetric states featuring long-range entanglement. Our results provide a unified perspective on recent studies of asymmetry in many-body physics, highlighting a nontrivial interplay between asymmetry, locality, and entanglement.

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Phys. Rev. Research 8, L012056– Published 6 March, 2026
  • Received 2 September 2025
  • Accepted 17 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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