Physicists Uncover Why Detecting Strong-to-Weak Symmetry Breaking May Be Impossible
Understanding Symmetry and Spontaneous Symmetry Breaking
Fundamental Concepts Behind Symmetry in Physics
When a system changes but a key physical property remains constant, that property is known as a "symmetry." Spontaneous symmetry breaking (SSB) happens when the system departs from this symmetry at most stable, lowest-energy state.
Physicists have recently discovered that a new form of SSB can arise in open quantum systems—those influenced by quantum effects and capable of exchanging energy, particles or information with their surroundings. They found that symmetry in such systems may be classified as either "strong" or "weak."
A strong symmetry means both the system and its environment individually uphold the symmetry, whereas a weak symmetry appears only when the two are considered together.
When a strong symmetry gives way to weak one, entirely new phases of matter may arise. Although this concept has attracted considerable theoretical interest, observing the shift from strong to weak symmetry has remained extremely difficult.
University of Texas Researchers Explore the Problem
A team at the University of Texas at Austin set out to determine whether it is genuinely possible to detect this strong-to-weak symmetry breaking in mixed states.
Their findings, published in Physical Review Letters, reveal that no efficient method can reliably identify the transition, as even advanced techniques struggle to differentiate certain symmetric states from those in which the symmetry has been broken.
"Physicists are constantly searching for fresh phases of matter," said co-authors Matteo Ippoliti and Xiaozhou Feng in an interview with Phys.org.
One of the most effective ways to understand different phases is through spontaneous symmetry breaking. In a solid, for instance, atoms break spatial symmetry by arranging themselves into a crystal lattice, whereas in a gas they can be found anywhere with equal likelihood.
"This form of symmetry breaking is spontaneous because it arises naturally from the atoms' interactions rather than being imposed externally, and it serves as a useful definition of what constitutes a phase of matter."
A Long-Standing Challenge in Modern Physics
Why SW-SSB Has Never Been Observed Experimentally
Strong-to-weak spontaneous symmetry breaking (SW-SSB) has emerged as a central theme in modern physics research. Yet, despite considerable interest, no experiment has successfully observed or confirmed this transition.
"One of the major challenges is simply determining whether a system truly exhibits SW-SSB," explained Ippoliti and Feng.
"In traditional symmetry breaking, the task is straightforward: an order parameter such as magnetization clearly indicates the phenomenon. But with SW-SSB, things become far more complex. Every proposed order parameter so far is an information-theoretic measure, and detecting it requires an impractically large—sometimes exponentially large—amount of experimental data."
Why Traditional and AI-Based Methods Fall Short
The study set out to uncover whether SW-SSB is fundamentally undetectable or if a more refined method might yet reveal it. To investigate this, the researchers drew on recent work in quantum cryptography, a field devoted to securing information through quantum mechanical principles.
"Our strategy is straightforward," the authors explained. "We 'encrypt' states that do not exhibit SW-SSB so effectively that no practical experiment can distinguish them from those that do."
"This demonstrates that no universal, efficient protocol for detecting SW-SSB can exist— because if it did, it would separate the two sets of states, contradicting the encryption."
The Breakthrough: Cryptography Reveals Fundamental Limits
Encryption as a Tool to Test Quantum Detectability
In their latest work, the team explore whether it was possible to create an encryption method that would leave the presence or absence of SW-SSB in mixed quantum states unchanged. They ultimately succeeded in doing so for two well-known symmetries: a discrete symmetry seen in certain magnetic systems and a continuous symmetry central to superconductivity.
Final Conclusions and Their Impact on Quantum Research
Drawing on quantum-cryptography techniques, Feng, Ippoliti and Cheng demonstrated that no current experimental protocol can reliably tell apart mixed quantum states that exhibit SW-SSB from those that do not. Their findings indicate that identifying this transition is inherently challenging, regardless of the tools employed. "Our research settles a major open problem: can SW-SSB be detected efficiently?" Feng and Ippoliti said.
"We show that, in the most general situation, the answer is negative: the order parameters scientists rely on today— often requiring exponentially large data sets—are essentially the best we can hope for without additional clues. This rules out scalable detection of these phases in quantum experiments, including those supported by AI or machine-learning tools."
Their findings could motivate new explorations of quantum many-body systems using ideas borrowed from cryptography. The team now plans to enhance the cryptographic techniques used in this study and extend them to future work.
Looking Ahead: Future Directions in Quantum Phase Detection
Moving Beyond the Black-Box Framework
"Our analysis is based on a 'black-box' framework that fits neatly within cryptography, though it is arguably les typical in physics," the authors said.
In this idealized scenario, an experimentalist receives copies of a quantum state with no additional information. In real-world settings, however, quantum experiments benefits from substantial prior knowledge about the system—insight that could be used to refine learning methods, including the possible detection of SW-SSB.
"Looking ahead, it will be valuable to incorporate more of this prior knowledge and better define what is required for efficient learning of phases of matter in open system. It may also prove fruitful to extend this framework to other phases or quantum phenomena."
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