Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group
arXiv:2510.09747 · doi:10.1103/48gw-6njm
The paper defines a spin coherence scale to quantify quantum coherence in spin systems, extending the quadrature coherence scale to SU(2)-invariant settings and linking it to nonclassicality, Wigner negativity, and rotation sensing applications.
Abstract
We introduce the spin coherence scale as a measure of quantum coherence for spin systems, generalizing the quadrature coherence scale (QCS) previously defined for quadrature observables. This SU()-invariant measure quantifies the off-diagonal coherences of a quantum state in angular momentum bases, weighted by the classical distinguishability of the superposed states. It serves as a witness of nonclassicality, provides both upper and lower bounds on the Hilbert-Schmidt distance to the set of classical (spin coherent) states, and bounds the Wigner negativity of a spin state. We demonstrate that many hallmark properties of the QCS carry over to the spin setting, including its links to noise susceptibility of a state and moments of quasiprobability distributions and its experimental realizability with a two-copy scheme. The spin coherence scale has direct implications for quantum metrology in the guise of rotation sensing. We also generalize the framework to SU() systems, identifying the unique SU()-invariant depolarization channel and outlining a broad, Lie-algebraic approach to defining and characterizing the properties of coherence scale beyond harmonic oscillators.
14+8 pages; 3 new authors + Wigner negativity and experimental connections; close to published version