On the table sits a glass of water. For each molecule, all directions are equivalent: it doesn't distinguish north from south. That's symmetry. But if you freeze the water, the molecules align into an ice lattice, and symmetry breaks: a preferred direction emerges.
The quantum world breaks symmetry more cunningly. The glass freezes, yet each molecule still tumbles randomly. Order is visible only in pairs, triples, or more complex groups of particles. This phenomenon is called strong-to-weak spontaneous symmetry breaking (SWSSB). It was long sought after and finally detected via special correlators — mathematical tools that reveal how much particles 'remember' each other.
The authors of the new work asked: does such partial order necessarily lead to the charge of an individual particle becoming indefinite, 'smeared' across the sample? Intuition says 'yes,' but the physicists checked mathematically. The link turned out not to be automatic. It all depends on how quickly correlations decay with distance. If they decay too slowly, the charge can remain almost localized, even though order exists in the system.
They constructed concrete examples where one exists without the other. The first example—'dephased superfluid': SWSSB is present, but charge variance doesn't grow with the size of the chunk — correlations decay too slowly. The second example—'sparse projectors onto fixed charge': here charge fluctuates strongly, but SWSSB is absent. The two phenomena, partial order and charge indeterminacy, are not twins but rather distant relatives who don't always visit together.
To sort out this zoo, the scientists devised a new correlator—'twisted overlap.' It acts as a filter, splitting charge fluctuations into two channels. The first channel is visible only through weak symmetry and accounts for coherent, 'clean' quantum jitters. The second is visible through strong symmetry and accounts for chaotic mixing. It turned out that the first channel is directly linked to the so-called skew information of Wigner–Yanase — a measure of how 'nonclassical' a quantum state is.
This approach provides a unified language for describing three different things: partial SWSSB order, local charge indeterminacy, and coherent charge fluctuations. Previously, they lived in separate mathematical rooms; now they can be studied in a common living room.
The Wigner–Yanase skew information that surfaced in this work was originally devised for quantum estimation theory — to determine how precisely a system's parameter can be measured. Now it helps distinguish types of quantum disorder.