{
  "annotation_id": "e58046f0-466c-4898-8dc5-81d622efc5e7",
  "date_created": "2026-03-02T18:02:37.759000Z",
  "date_modified": "2026-03-02T18:02:37.759000Z",
  "file_hash": "fe1c6a7df899e61b8bc51c058ffc1d63a895604bed4c0c449c6ea940ff35a4e6",
  "private": false,
  "record": {
    "abstract": "Quantum Error Correction will be necessary for preserving coherent states\nagainst noise and other unwanted interactions in quantum computation and\ncommunication. We develop a general theory of quantum error correction based on\nencoding states into larger Hilbert spaces subject to known interactions. We\nobtain necessary and sufficient conditions for the perfect recovery of an\nencoded state after its degradation by an interaction. The conditions depend\nonly on the behavior of the logical states. We use them to give a recovery\noperator independent definition of error-correcting codes. We relate this\ndefinition to four others: The existence of a left inverse of the interaction,\nan explicit representation of the error syndrome using tensor products, perfect\nrecovery of the completely entangled state, and an information theoretic\nidentity. Two notions of fidelity and error for imperfect recovery are\nintroduced, one for pure and the other for entangled states. The latter is more\nappropriate when using codes in a quantum memory or in applications of quantum\nteleportation to communication. We show that the error for entangled states is\nbounded linearly by the error for pure states. A formal definition of\nindependent interactions for qubits is given. This leads to lower bounds on the\nnumber of qubits required to correct $e$ errors and a formal proof that the\nclassical bounds on the probability of error of $e$-error-correcting codes\napplies to $e$-error-correcting quantum codes, provided that the interaction is\ndominated by an identity component.",
    "arxiv_id": "quant-ph/9604034",
    "authors": [
      "Emanuel Knill",
      "Raymond Laflamme"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.84.2525",
    "journal_ref": "Phys.Rev.Lett.84:2525-2528,2000",
    "title": "A Theory of Quantum Error-Correcting Codes",
    "url": "https://arxiv.org/abs/quant-ph/9604034"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "af053197-b1cd-4c7d-965c-81a7c3eb1c99",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}