Characterising strong-to-weak spontaneous symmetry breaking (SW-SSB) previously relied on methods unable to detect order when conventional correlations vanish; however, SW-SSB now consistently appears as a shortfall in quantum Fisher Information (QFI). An inequality links this deficit, Ds, with fidelity and Rényi-1 correlators as indicators of long range order. The team showed locality ensures this geometric constraint persists even at finite temperatures. A new method detects “strong-to-weak” spontaneous symmetry breaking, a key phenomenon for understanding quantum systems, when standard techniques fail.

This type of symmetry breaking is linked to Quantum Fisher Information, essentially how much information can be extracted from a quantum state via specific rotations. This approach reliably characterizes these phases regardless of temperature or distance and offers an alternative diagnostic tool when conventional measurements are ineffective. Researchers unveiled a technique to detect “strong-to-weak” spontaneous symmetry breaking, a key phenomenon for understanding quantum systems, even when traditional methods fail; it’s akin to identifying subtle shifts in order within complex arrangements where standard measurements offer no clear signal.

The approach links symmetry breaking to QFI, which measures how precisely we can determine parameters within a quantum system, much like assessing the focus and clarity of a microscope on minute details. The team demonstrated that strong-to-weak symmetry breaking manifests as a consistent shortfall in this QFI, linking this deficit with indicators of long range order such as Rényi-1 correlators, which capture connections between distant parts of a system similar to detecting unspoken influence among individuals across a room.

Quantum Fisher Information Deficits Quantify Symmetry Breaking at Finite Temperatures

Quantum Fisher Information (QFI) deficits consistently fall below their algebraic maximum, specifically, this deficit, Ds, is always greater than or equal to *e -2βJO *, where β represents inverse temperature and JO defines a system’s local Hamiltonian bounds. Offering new diagnostic tools when conventional methods fail due to vanishing correlations, locality keeps the energy cost associated with measuring this QFI difference uniformly bounded regardless of system size or distance between points being measured. This ensures a finite gap remains below maximum possible information even at fixed temperatures.

Characterising Hidden Order via Quantum Fisher Information Reduction

A measure of how precisely parameters within a quantum system can be estimated, Quantum Fisher Information (QFI) was used not for accelerating detection but to identify a consistent shortfall from its maximum value. The technique involved subjecting strongly symmetrical quantum states to subtle “pair rotations,” manipulating them in a way that preserved overall symmetry while probing for hidden order. Carefully measuring the reduction in maximal QFI under these specific rotations allowed characterisation of spontaneous symmetry breaking, even when conventional methods failed because standard indicators like long-range correlations were absent.

Spontaneous symmetry breaking (SW-SSB) has been established as a framework for describing quantum phases in open systems; however, SW-SSB cannot be characterised by conventional charged two-point correlators. For strongly Z 2 -symmetric states with local charged involutions, this work demonstrates that SW-SSB manifests as a persistent deficit from the maximal Quantum Fisher Information (QFI) under symmetry-neutral pair rotations. An inequality hierarchy connects this QFI deficit to fidelity and Rényi-1 correlators, establishing their equivalence as asymptotic long-range order diagnostics.

This connection links finite-angle state overlaps to constraints on Bures geometry along rotation orbits, and locality keeps the energy cost bounded regardless of system size or endpoint separation, maintaining a gap below maximum QFI at any fixed temperature. When conventional charged long range order is absent, this persistent geometric constraint provides an information-geometric characterisation of thermal SW-SSB. Widely used in areas like quantum metrology and many-body phase studies, Quantum Fisher Information (QFI) characterizes how precisely parameters within a quantum system can be estimated. Recent work explored using QFI to study traditional spontaneous symmetry breaking. Instead of maximising the QFI, this approach examines changes in information regarding paired particles under rotation, measuring how far short it falls from its theoretical maximum value. This measure offers an alternative when methods reliant on long range correlations fail while studying complex systems.

This research demonstrated that spontaneous symmetry breaking, a phenomenon describing shifts in quantum phases, can be identified by consistently lower than expected Quantum Fisher Information (QFI) values during specific rotations applied to pairs of particles. The study found a connection between this reduction in QFI and other measurements like fidelity and Rényi-1 correlators, offering new ways to detect order within systems where traditional indicators are absent.

By examining the energy cost associated with these particle operations, researchers established a quantifiable characteristic for thermal spontaneous symmetry breaking independent of system size or temperature. This approach provides an information-geometric method for characterizing such phase transitions when conventional methods fail.

👉 More information
🗞 Quantum Fisher Information Deficit as a Geometric Signature of Strong-to-Weak Spontaneous Symmetry Breaking
✍️ Zhang-Chi Yin and Wei Zheng (University of Science and Technology of China)
🧠 ArXiv: https://arxiv.org/abs/2610.37092

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