Homequant-pharXiv:2605.29436

Total, quantum, and classical measures of anticoherence for mixed spin states

quant-ph2026-05v1license

Abstract

Anticoherent spin states have isotropic low-order spin moments and are relevant to direction-independent metrology and quantum reference-frame alignment. In contrast to pure states, for mixed states such isotropy may originate either from genuine quantum correlations or from classical statistical mixing. We introduce an axiomatic framework for mixed-state tt-anticoherence based on the symmetric qubit embedding. We distinguish total tt-anticoherence, non-decreasing under SU(2)-covariant channels, from quantum tt-anticoherence, defined as a resource monotone relative to a chosen total measure and constrained to coincide with it on pure states. This yields a classical contribution as their difference. We construct total measures based on reduced-state purity, Hilbert-Schmidt distance, and cumulative multipoles, and we discuss fidelity-based total candidates. We construct quantum counterparts via convex-roof extensions of pure-state functionals tied to bipartite entanglement in the symmetric sector. We provide explicit mixed-state examples, identify states with maximal quantum anticoherence supported on anticoherent subspaces, study robustness under particle loss for different types of states, and characterize the trade-off between purity and the maximal achievable anticoherence order.

Comments: 19 pages, 3 figures, 1 table

Cite

@article{arxiv.2605.29436,
  title  = {Total, quantum, and classical measures of anticoherence for mixed spin states},
  author = {Jérôme Denis and Tara Lacaille and John Martin and Eduardo Serrano-Ensástiga},
  journal= {arXiv preprint arXiv:2605.29436},
  year   = {2026}
}