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PreprintCC0arXiv

Geometric Characterization and Feasible Region Analysis of Bipartite Qutrit Bound Entanglement

  • Mazhar Ali
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Abstract

We characterize bound entanglement in bipartite qutrit systems by combining the Positive Partial Transpose (PPT) criterion with a structural, non-completely positive map. Focusing on a comprehensive three-parameter bipartite qutrit family ρa,b,c, we present an exact analytical and geometric partitioning of the physical state space simplex. We derive the closed-form quadratic boundary governing the leaf-like PPT region (a2+ab+b2−b ≤ 0) over the domain 0 < a ≤ 1/3, and identify the exact linear threshold (a > c) that characterizes the PPT bound entangled sub-region. This family strictly generalizes the well-known Horodecki bound entangled states, which appear as a single slice of the three-dimensional leaf. Applying the structural map to this decomposition, we show that it certifies bound entanglement throughout the entire threshold region, accounting for 14.76% of the total PPT leaf area.

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Cite

BibTeXRIS
BibTeX
@misc{ali2026geometric,
  title = {{Geometric Characterization and Feasible Region Analysis of Bipartite Qutrit Bound Entanglement}},
  author = {Mazhar Ali},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39141},
  eprint = {2609.39141},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39141},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Geometric Characterization and Feasible Region Analysis of Bipartite Qutrit Bound Entanglement
AU  - Mazhar Ali
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39141
UR  - https://arxiv.org/abs/2609.39141
AB  - We characterize bound entanglement in bipartite qutrit systems by combining the Positive Partial Transpose (PPT) criterion with a structural, non-completely positive map. Focusing on a comprehensive three-parameter bipartite qutrit family ρ_a,b,c, we present an exact analytical and geometric partitioning of the physical state space simplex. We derive the closed-form quadratic boundary governing the leaf-like PPT region (a^2+ab+b^2−b ≤ 0) over the domain 0 < a ≤ 1/3, and identify the exact linear threshold (a > c) that characterizes the PPT bound entangled sub-region. This family strictly generalizes the well-known Horodecki bound entangled states, which appear as a single slice of the three-dimensional leaf. Applying the structural map to this decomposition, we show that it certifies bound entanglement throughout the entire threshold region, accounting for 14.76% of the total PPT leaf area.
ER  -