[
  {
    "id": "ARR-2026-0DHZ1VS2VR9K7T4M-v1",
    "type": "article",
    "title": "Sharp positivity orders for reduction maps on perfect-tensor codes",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          25
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-0DHZ1VS2VR9K7T4M",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-0DHZ1VS2VR9K7T4M/versions/v1/",
    "note": "Research preprint; ARR-2026-0DHZ1VS2VR9K7T4M v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We classify positivity of tensor products of reduction maps after restriction to perfect-tensor codes. For encodings from AME(4,d), the restricted Choi matrix splits into an isotropic code-output block and a completely positive complement. This gives the exact rank-constrained minimum for every parameter between zero and one. For every AME(6,d), an operator bound obtained from five incident-error stars proves an exact simple least Choi eigenvalue and a monotone quintic complete-positivity threshold. At the half parameter, its complementary output block is also completely positive, giving an exact positivity-order classification. Uniformly in the code dimension, the encoded three- and five-copy maps are respectively 8-positive and 32-positive. Exact code-projector witnesses show that these orders cannot be increased to 9 and 33. The entire column support must lie in the code; the opposite support is free. The results do not imply positivity of unrestricted physical tensor powers or allow tensorization of merely k-positive maps. We separate a classical low-rank PPT explanation of qutrit entanglement breaking from an explicit Weyl measure-and-prepare realization."
  }
]