trureturing — Discovering truth

bibkey: tran2026spectralappt authors: Anh T. Tran year: 2026 title: “Spectral Optimization for Absolutely PPT States: Purity, Entropy, and Volume Decay” doi: 10.48550/arXiv.2609.18568 url: https://arxiv.org/abs/2609.18568v1 claim: “Theorem A gives a strict qutrit outer purity bound; the remark following it leaves exact maximum APPT purity open.” strata_touched:

• D5/S3/Quantum/Entanglement/AbsolutePPT/QutritQuditMaximumPurity license: citation-only triage: anchor

Verified locator

DOI: https://doi.org/10.48550/arXiv.2609.18568

Source: https://arxiv.org/abs/2609.18568v1

Remark following Theorem A

Page 4, verbatim source statement:

Determining the exact maximum APPT purity remains open.

The same remark states, verbatim:

Hence the inequality in Theorem A is strict for every $3\otimes n$ system with $n\ge 3$, and the Dũng–Khôi conjecture is false in those dimensions.

The strict outer bound and the falsity of the Dũng–Khôi candidate are source results. They are distinct from the inscribed-polytope equality in Ahiable–Kothakonda–Winter Conjecture 6.7.