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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.
Physical Review Letters
|November 30, 2025
Summary
Detecting strong-to-weak spontaneous symmetry breaking (SSB) in quantum systems is challenging. This study shows efficient detection is generally impossible, even for Z2 and U(1) symmetries, due to indistinguishable pseudorandom states.
Area of Science:
- Quantum physics
- Condensed matter physics
- Quantum information
Background:
- Spontaneous symmetry breaking (SSB) is fundamental to quantum phases of matter.
- SSB in mixed states of open quantum systems can be strong or weak.
- Novel quantum phases arise from strong-to-weak SSB.
Purpose of the Study:
- To investigate the efficient detectability of strong-to-weak SSB.
- To determine if general, efficient protocols exist for detecting this phenomenon.
- To explore the limitations in identifying novel mixed-state quantum phases.
Main Methods:
- Construction of pseudorandom mixed state ensembles.
- Analysis of Z_{2} and U(1) symmetry breaking in quantum systems.
- Computational indistinguishability tests for quantum states.
Main Results:
- Efficient detection of strong-to-weak SSB is shown to be generally impossible.
- Pseudorandom states were created that mimic strong-to-weak SSB without actually occurring.
- These states are computationally indistinguishable from true SSB states.
Conclusions:
- Efficient, state-agnostic protocols for detecting strong-to-weak SSB cannot exist.
- The study rules out general efficient detection methods for these novel quantum phases.
- Understanding the limits of detection is crucial for characterizing mixed-state quantum matter.
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