Metadata
bibkey: rossetti2025observational
authors: L. Rossetti; S. Mancini; A. Winter; J. Schindler
year: 2025
title: Observational entropy of quantum correlations and entanglement
doi: 10.1109/TIT.2026.3700031
url: https://arxiv.org/abs/2510.10058v1
claim: "The membership of the optimal three-qubit W-state PPT POVM in SEP is posed as an open question."
strata_touched:
- D5/S3/Quantum/Measurement/RossettiW3PPTMeasurement
license: citation-only
triage: anchor
Verified locator
DOI: https://doi.org/10.1109/TIT.2026.3700031
Source: https://arxiv.org/abs/2510.10058v1
The cited text is arXiv v1, Sections IX and X.0.4, equations (62), (79), and (83), printed pages 17, 22, and 23. The IEEE journal text has not been verified.
Source statements
Page 17, immediately after equation (62):
In other words, the POVM elements are proportional to separable states.
Page 22:
the invariant operators can be shown to be linear combinations of six projectors: Q₁ = |W₃⟩⟨W₃|, Q₂ = |W̄₃⟩⟨W̄₃|, Q₃ = P₁ − W₃, Q₄ = P₂ − W̄₃, Q₅ = |000⟩⟨000|, and Q₆ = |111⟩⟨111|
Page 23:
Proving that (M′, 𝟙 − M′) belongs to the SEP class—i.e., showing that both M′ and 𝟙 − M′ are fully separable—would yield an analytic value for E_SEP(W₃) as well.
Nevertheless, none of the tests conducted so far have succeeded in detecting entanglement, leaving open the question of whether (M′, 𝟙 − M′) belongs to the SEP class.
The three-qubit basis is indexed by functions Fin 3 → Fin 2, listing the three
bits in their site order. The operator M′ has coefficients
t₂ = 1/2, t₃ = t₄ = 0, t₅ = 2/3, t₆ = 1/12 in equation (83).
The corresponding Lean result refutes membership of this particular two-outcome
measurement in SEP. It does not determine the optimal SEP observational entropy.
Evidence boundary
The exact-arithmetic experiment is in
trureturing-experiments.
Its check.py SHA-256 is
0f67cf8ea123698ede88939d2587f06c93af4e49b152631a40e04528acb29659;
python3 check.py exits 0 with RESULT PASS 0 as reported in issue #19016.
Its checks of the complementary operator and its partial transposes being positive,
and of a separable decomposition of M′, are computed evidence, distinct from the
Lean refutation. Literature-screen completeness and the journal version’s question
status are ASSUMED-UNVERIFIED.