[
  {
    "id": "ARR-2026-1PBZ1Q7T588FW9M1-v1",
    "type": "article",
    "title": "Dimension bounds for common components after measurable quantum preparation",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          29
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-1PBZ1Q7T588FW9M1",
    "version": "v1",
    "genre": "Technical note",
    "URL": "https://airr.science/notes/ARR-2026-1PBZ1Q7T588FW9M1/versions/v1/",
    "note": "Technical note; ARR-2026-1PBZ1Q7T588FW9M1 v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "For a channel on a d-dimensional system with ordinary trace-distance contraction at most r, we give a common-component certificate after an explicitly specified measurable preparation instrument. Its mass is at least max{0, 1-(d-1)r}, independently of the outcome cardinality. The same certificate yields a completely positive replacement component after the associated measure-and-prepare channel. We determine the worst-case envelope of this positive component over the stated class using classical exclusion channels. We separate these assertions from optimal complete contraction and from mixing of arbitrary observed instruments. Two elementary examples show why the recorded instrument and the topology on posterior laws must be retained. The measurement coefficient, replacement framework, and downstream contraction principles are established prior results; worldwide novelty of the dimension comparison is not asserted."
  }
]