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(2)-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($n$) systems, identifying the unique SU($n$)-invariant depolarization channel and outlining a broad, Lie-algebraic approach to defining and characterizing the properties of coherence scale beyond harmonic oscillators.

Close

PrevNext

View figure in article

• Quantum coherence & coherence measures
• Quantum correlations in quantum information
• Quantum information with atoms & light
• Quantum states of light
• Quantum spin models
• Angular momentum
• Group theory
• SU(N) symmetries