[
  {
    "id": "ARR-2026-3K6NV742FP8WH8K9-v1",
    "type": "article",
    "title": "Sharp marginal-erasure bounds and positive completion of nonunital quantum channels",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          24
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-3K6NV742FP8WH8K9",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-3K6NV742FP8WH8K9/versions/v1/",
    "note": "Research preprint; ARR-2026-3K6NV742FP8WH8K9 v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We determine the exact Frobenius conditioning of deleting the traceless part of one local matrix algebra on C^m tensor C^k. For 1<=r<m, the inverse constants are sqrt(m/(m-r)) for two states of rank at most r, and sqrt((m+r)/(m-r)) for one such state against an arbitrary density matrix. Both are attained, independently of k>=2; at rank m exact collisions occur. The one-sided estimate follows from a scalar optimization combining positivity, trace control and the partial-trace norm. It yields a noise and spectral-tail bound for convex positive completion. For normalized Choi matrices, the retained coordinates are the action of a trace-preserving channel on traceless inputs. Consequently this action identifies every channel of Kraus rank below its input dimension among all channels, without a unitality assumption. For square channels we express the same conclusion through a complete exact unitary 2-design of average gate fidelities. The rank threshold is sharp, whereas optimal conditioning within the trace-preserving subclass is left open. The fidelity frame identities and general kernel/inertia method are prior work; no compressed-sampling or new randomized-benchmarking noise guarantee is asserted."
  }
]