[
  {
    "id": "ARR-2026-58XZ9SCZA39DSRF0-v1",
    "type": "article",
    "title": "Constant-gap entanglement distillation and a spectral criterion for noise-universal communication",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          18
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-58XZ9SCZA39DSRF0",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-58XZ9SCZA39DSRF0/versions/v1/",
    "note": "Research preprint; ARR-2026-58XZ9SCZA39DSRF0 v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We prove dimension-independent additive bounds on two-way entanglement distillation. For every conjugate local diagonal unitary invariant state, distillable entanglement, secret key and relative entropy of entanglement lie in an explicitly computable interval of width at most log2(5) bits per copy. For the broader class invariant under local diagonal signs, the diagonal-relative-entropy reference exceeds distillable entanglement by at most log2(9). The proof uses established partial breeding with a stopped classification whose entropy is bounded independently of dimension; a reduction-based seed pays for all initial assistance. The resulting recovery bound also implies at most log2(6) ebits of irreversibility for any mixture of a pure state and separable noise, without a marginal constraint, and controls mixtures with a mixed maximally correlated component. For an identity component mixed with arbitrary channel noise, we give six capacity guarantees and reduce their simultaneous worst cases to depolarizing channels. An explicit isotropic interval has absolute width tending to 2(1-f) at fixed entangled fraction f, refining the known relative large-dimension approximation. For general discrete Hamiltonians with a finite partition sum at some temperature, we identify the exact spectral boundary of absolute entanglement-assisted recovery: for each fixed reset state, the loss vanishes precisely when the partition sum diverges at its critical inverse temperature. In that regime all six capacities attain their erasure benchmarks with absolute o(1) loss. In the complementary regime every fixed reset has a strictly positive limiting assisted deficit, given by a critical-Gibbs variational formula. An explicit integer spectrum has an exact constant-loss plateau. The reset may have infinite energy or entropy. Oscillator consequences include reversible distributed states and a vanishing classical arbitrary-partner additivity defect. Optimal constants, efficient implementations and general exact finite-energy capacities remain unresolved."
  }
]