Kavli Affiliate: Mazhar Ali
| Summary:
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 $(a^2+ab+b^2-b leq 0)$ over the domain $0 < a leq frac13$, 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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