bibkey: denisetal2026anticoherencemixed
authors: Jérôme Denis, Tara Lacaille, John Martin and Eduardo Serrano-Ensástiga
year: 2026
title: "Total, quantum, and classical measures of anticoherence for mixed spin states"
doi: 10.48550/arXiv.2605.29436
url: "https://arxiv.org/abs/2605.29436v1"
claim: "The paper axiomatizes total t-anticoherence measures for mixed spin-j states, including monotonicity (T4) under SU(2)-covariant channels, proves (T4) for the Hilbert–Schmidt distance-based measure, and leaves open whether (T4) holds for the trace-distance-based measure."
strata_touched:
  - D5/S3/Quantum/Measurement/AnticoherenceTraceDistanceRefutation
license: citation-only
triage: anchor

Denis, Lacaille, Martin and Serrano-Ensástiga, Total, quantum, and classical measures of anticoherence for mixed spin states

J. Denis, T. Lacaille, J. Martin and E. Serrano-Ensástiga, arXiv:2605.29436v1 (2026). Quotations are from the v1 TeX source.

A spin-$j$ state $\rho$ is identified with a symmetric state ${\rho }_S$ of $N=2j$ qubits, and ${\rho }_t={\mathrm{Tr}}_{N-t}({\rho }_S)$ is its $t$-qubit reduction, defined for every $t\in \{1,\dots ,N\}$. A total $t$-anticoherence measure must satisfy, among other axioms,

(T4) Monotonicity under $\mathrm{SU}(2)$-covariant noise: For every $\mathrm{SU}(2)$-covariant channel $\Phi :\mathcal{D}({\mathcal{H}}_j)\to \mathcal{D}({\mathcal{H}}_j)$, […] one has ${\mathcal{A}}_t^T(\Phi (\rho ))\ge {\mathcal{A}}_t^T(\rho )$ for all $\rho \in \mathcal{D}({\mathcal{H}}_j)$.

The distance-based candidates are ${\mathcal{A}}_t^{T,d}(\rho )=1-d({\rho }_t,1_{t+1}/(t+1))/K_t$ with $K_t$ the largest possible distance. After proving (T4) for the Schatten-2 distance, the paper states:

We also find numerical evidence that axiom (T4) remains valid for the trace-distance case $p=1$; a proof is left open.

Verified locator

Source: https://arxiv.org/abs/2605.29436v1

• DOI: https://doi.org/10.48550/arXiv.2605.29436 (the arXiv-issued DataCite DOI; title, authors and year from DataCite; the abstract page lists v1 only).
• URL: https://arxiv.org/abs/2605.29436v1. The e-print member arxiv.tex has 1647 lines and md5 cc8e7241680606ee66e21581554aa985. Locations:
  • the symmetric-subspace identification and ${\rho }_t$, l. 150–161;
  • the range of $t$, footnote at l. 178;
  • axiom (T4), l. 180–200;
  • distance-based measures, l. 333–358;
  • Proposition 2 and the open trace-distance case, l. 359–363.