Quantum-information fingerprints of partial dynamical symmetry in the interacting boson model

Abstract:Partial dynamical symmetry (PDS) is an algebraic structure in which a prescribed symmetry is neither exact nor completely broken: a subset of eigenstates keeps good quantum numbers and remains solvable while the rest of the spectrum mixes. PDS is currently identified from spectroscopic data, band-head energies, level systematics, and $B(E2)$ ratios. We ask whether it also has a purely structural signature in the eigenstates, and find that it does, though not in the magnitude of entanglement. The natural diagnostic is the variance of a symmetry Casimir, the label variance $\Var\,\C[G]$, which we show coincides with a block-coherence entropy and a block impurity: all three vanish exactly when a state carries a single irreducible-representation label. Resolved state by state, this quantity is zero on the solvable subset and of order $N^2$ on the mixed states, at stable symmetry points and at Leviatan's first- and second-order critical points, where it takes two distinct forms set by the order of the transition. The magnitude of bipartite entanglement, by contrast, does not separate solvable from mixed states and drifts even where the labels are exact. We anchor the analysis in $^{168}$Er, connect the block purity to the ``purity/coherence'' language of the quasi-dynamical-symmetry literature, and show the label variance is uncorrelated with multipartite entanglement and with magic. Finally we encode the model on a qubit register and prepare its solvable and mixed eigenstates variationally, as a step toward evaluating the diagnostic on a quantum device.

arXiv:2608.04486 [quant-ph]

(or arXiv:2608.04486v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.04486 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.