bibkey: guo2024completegenuine
authors: Y. Guo
year: 2024
title: Complete Genuine Multipartite Entanglement Monotone
doi: 10.1016/j.rinp.2024.107430
url: https://arxiv.org/abs/2301.00334v3
claim: "Equation (24) conjectures subadditivity of the reduced function ĥ(ρ) = √(δ1 δ2), where δ1 and δ2 are the two largest eigenvalues of ρ."
strata_touched:
  - D5/S3/Quantum/Entanglement/PartialNegativity/GuoHatSubadditivityRefutation
license: citation-only
triage: anchor

Guo, Complete Genuine Multipartite Entanglement Monotone

Results in Physics 57 (2024), 107430; arXiv:2301.00334v3 (19 August 2025).

Verified locator

DOI: 10.1016/j.rinp.2024.107430

Source: https://arxiv.org/abs/2301.00334v3

Source statements

Pages 4–5, the reduced function of the partial negativity:

ĥ(ρ) = √(δ1 δ2), … and δ1, δ2 are the two largest eigenvalues of ρ.

Page 5, equation (24):

We conjecture that ĥ is subadditive, i.e., ĥ(ρAB) ⩽ ĥ(ρA) + ĥ(ρB) (24) holds for any ρAB ∈ S^{AB}. In what follows, we always assume that hF′, hAF, and ĥ are subadditive, and that ĥ is concave.

Table I marks this subadditivity with “We conjecture that they are subadditive.” The two eigenvalues are ordered decreasingly with multiplicity. The reduced states are the partial traces of the same joint density matrix.

Scope and literature boundary

The source defines the function and states its subadditivity as a conjecture. The repository’s counterexample is a mixture of two orthogonal maximally entangled states on a 5 × 5 system. Its value is 1/2 and the marginal values are each 1/5. This refutes the unrestricted conjecture; universal validity in local dimensions at most four remains open here.

Literature completeness is ASSUMED-UNVERIFIED. The preregistration at https://github.com/the-omega-institute/trureturing/issues/19494 records a partial screen of the arXiv versions and eight accessible citing works. The published paper and erratum full texts, and Guo, Physical Review A 110, 012405 (2024), were unread in that screen. The erratum abstract concerns equations (36), (37), (39), (41), and (43); the later arXiv v3 retains conjecture (24).