Sparse positive maps on qutrits with exact nondecomposability thresholds and PPT-entanglement transitions

• URL: http://arxiv.org/abs/2606.19765v1
• Date: Thu, 18 Jun 2026 03:56:21 GMT
• Title: Sparse positive maps on qutrits with exact nondecomposability thresholds and PPT-entanglement transitions
• Abstract summary: We study a family of sparse positive maps on qutrits for which positivity, decomposability, and PPT entanglement can all be analysed explicitly.<n>For the same families we determine the exact transition between decomposable and non-decomposable maps.<n>For the trace-preserving subclass, we compare positivity with a recent eigenvalue bound for 2-positive maps, thereby making the gap between positivity and higher-order positivity fully explicit within this family.
• Score: 0.6157382820537719
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study a family of sparse positive maps on qutrits for which positivity, decomposability, and PPT entanglement can all be analysed explicitly. The block structure of the associated Choi matrices reduces positivity to a Hermitian biquadratic form and leads to exact positivity boundaries for three representative parametric families. For the same families we determine the exact transition between decomposable and non-decomposable maps and construct associated PPT states of two classes. The first consists of witness-adapted deformations naturally tied to the non-decomposability analysis. The second consists of analytically tractable families whose full PPT-entangled branch is detected by fixed positive maps, yielding exact thresholds between separability and bound entanglement. For the trace-preserving subclass, we further compare positivity with a recent eigenvalue bound for 2-positive maps, thereby making the gap between positivity and higher-order positivity fully explicit within this family.

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