Metadata
bibkey: wangchensong2026extremeappt
authors: Nalan Wang; Lin Chen; Zhiwei Song
year: 2026
title: "Extreme points of absolutely PPT states with exactly three distinct eigenvalues"
doi: 10.1088/1402-4896/ae9148
url: https://arxiv.org/abs/2603.20717v1
claim: "Fourth, what is the achievable upper bound of distinct eigenvalues of extreme two-qutrit AP states?"
strata_touched:
- D5/S3/Quantum/Entanglement/AbsolutePPT/QutritExtremeSixLevels
license: citation-only
triage: anchor
Verified locator
DOI: https://doi.org/10.1088/1402-4896/ae9148
Source: https://arxiv.org/abs/2603.20717v1
Journal reference: Physica Scripta 101 (2026), 315210.
Source question
Section VII, Conclusions, page 29, asks:
Fourth, what is the achievable upper bound of distinct eigenvalues of extreme two-qutrit AP states?
The state space consists of positive semidefinite, trace-one operators on . Absolute PPT requires the partial transpose of every global unitary conjugate to be positive semidefinite. Extremality means membership in the extreme points of the convex set of those states. Distinct eigenvalues are counted without multiplicity.
The answer formalized in QutritExtremeSixLevels is six, including attainment. The journal edition’s full text remains ASSUMED-UNVERIFIED; the arXiv source contains the quoted question.
State definition
Definition 1, page 3:
A separable (resp. PPT) state ρ is called absolutely separable (resp. PPT) if it remains separable (PPT) regardless of what global unitary operation is applied. That is, for any unitary matrix U, the state UρU† is separable (resp. PPT).
The formalization uses the PPT case. Density matrices are positive semidefinite and have trace one; the partial transpose is taken on the second local factor.