Scalable Spin Squeezing from Finite Temperature Easy-plane Magnetism

TL;DR

This paper demonstrates that finite temperature easy-plane ferromagnetic Hamiltonians can generate scalable spin squeezing, advancing quantum sensing by linking phase transitions with entanglement properties.

Contribution

It provides numerical and analytic evidence connecting easy-plane ferromagnetism at finite temperature with the ability to produce scalable spin squeezing for quantum metrology.

Findings

Spin squeezing exhibits a phase transition aligned with XY order boundary.

Scalable squeezing achieves sensitivity between SQL and all-to-all models.

Short-range two-axis twisting cannot produce scalable metrological gain.

Abstract

Spin squeezing is a form of entanglement that reshapes the quantum projection noise to improve measurement precision. Here, we provide numerical and analytic evidence for the following conjecture: any Hamiltonian exhibiting finite temperature, easy-plane ferromagnetism can be used to generate scalable spin squeezing, thereby enabling quantum-enhanced sensing. Our conjecture is guided by a connection between the quantum Fisher information of pure states and the spontaneous breaking of a continuous symmetry. We demonstrate that spin-squeezing exhibits a phase diagram with a sharp transition between scalable squeezing and non-squeezing. This transition coincides with the equilibrium phase boundary for XY order at a finite temperature. In the scalable squeezing phase, we predict a sensitivity scaling that lies in between the standard quantum limit and the scaling achieved in all-to-all coupled one-axis twisting models. A corollary of our conjecture is that short-ranged versions of two-axis twisting cannot yield scalable metrological gain. Our results provide insights into the landscape of Hamiltonians that can be used to generate metrologically useful quantum states.