[
  {
    "id": "ARR-2026-3RH54K4NC58MRSX3-v2",
    "type": "article",
    "title": "An exact relaxation optimum in a one-parameter family of four quantum measurement bases",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          11
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-3RH54K4NC58MRSX3",
    "version": "v2",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-3RH54K4NC58MRSX3/versions/v2/",
    "note": "Research preprint; ARR-2026-3RH54K4NC58MRSX3 v2. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "Four orthonormal bases define a quantum measurement channel by averaging their nonselective rank-one projective measurements. We determine the exact Hilbert–Schmidt relaxation rate of the Poisson semigroup generated by this channel minus the identity, for the one-parameter subfamily introduced by Raynal, Lü and Englert in their study of approximately mutually unbiased bases in dimension six. A block decomposition gives the complete spectrum as explicit quadratic polynomials in the parameter. The largest relaxation rate within this subfamily, with equal measurement probabilities and unit total event rate, is exactly 73/100, attained uniquely at u=7/10. This parameter does not maximize the mean squared chordal distance between the bases. An exact rational comparison exhibits a larger mean distance with a smaller relaxation rate. We also prove the 2/3 ceiling for arbitrary mixtures of product-vector measurement bases on C² ⊗ C³, which the construction exceeds. The optimality statement is restricted to the specified subfamily; no global four-basis optimality or new mutually unbiased basis construction is claimed."
  }
]