Breaking global symmetries with locality-preserving operations

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 Δ⁢𝑆𝐺 𝑁, 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, Δ⁢𝑆𝐺 𝑁≤(1/2)⁢Δ⁢𝑆𝐺,max 𝑁⁢[1+𝑜⁡(1)], where Δ⁢𝑆𝐺,max 𝑁 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, Δ⁢𝑆𝐺 𝑁∼Δ⁢𝑆𝐺,max 𝑁, 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.