Robust spin-squeezing on quantum networks: the lesson from universality

TL;DR

This paper explores the conditions for scalable spin squeezing in quantum networks with complex geometries, linking universal properties of interaction graphs to metrological performance.

Contribution

It introduces a theoretical framework connecting spectral dimension and universality classes to spin squeezing scalability in inhomogeneous quantum networks.

Findings

Scalable squeezing governed by the spectral dimension of the interaction graph.

Critical squeezing depends on the interplay between universality classes.

Provides conditions for robust metrological gain in various experimental setups.

Abstract

We establish the conditions under which scalable spin squeezing can be achieved in interacting spin ensembles embedded in arbitrary, inhomogeneous network geometries. We identify two different forms of squeezing: OAT-like scalable squeezing is governed solely by the universal properties of the interaction graph and is controlled by its spectral dimension. In critical squeezing, on the other hand, the value of the spectral dimension only furnishes the necessary condition for scalable metrological gain, while the sufficient condition requires the model to lie below the symmetry breaking transition. Therefore, in quantum networks, the scaling of the spin-squeezing critical point emerges from a nontrivial interplay between xy-ferromagnetic universality and percolation universality. We apply this general theoretical framework to several experimental scenarios and discuss sharp and experimentally relevant conditions for achieving robust metrological gain on generic inhomogeneous structures, giving a unifying perspective for designing scalable quantum sensors across diverse quantum simulation platforms.