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Updated: Jan 9, 2026

Determining the Mechanical Strength of Ultra-Fine-Grained Metals
Published on: November 22, 2021
Hardness of Observing Strong-to-Weak Symmetry Breaking
Xiaozhou Feng1, Zihan Cheng1, Matteo Ippoliti1
1The University of Texas at Austin, Department of Physics, Austin, Texas 78712, USA.
Abstract:
Spontaneous symmetry breaking (SSB) is the cornerstone of our understanding of quantum phases of matter. Recent works have generalized this concept to the domain of mixed states in open quantum systems, where symmetries can be realized in two distinct ways dubbed strong and weak. Novel intrinsically mixed phases of quantum matter can then be defined by the spontaneous breaking of strong symmetry down to weak symmetry. However, proposed order parameters for strong-to-weak SSB (based on mixed-state fidelities or purities) seem to require exponentially many copies of the state, raising the question: Is it possible to efficiently detect strong-to-weak SSB, in general? Here, we answer this question negatively in the paradigmatic cases of Z_{2} and U(1) symmetries. We construct ensembles of pseudorandom mixed states that do not break the strong symmetry yet are computationally indistinguishable from states that do. This rules out the existence of efficient state-agnostic protocols to detect strong-to-weak SSB.
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