{
  "annotation_id": "cebf1520-c9ec-4a83-a041-a76622485a1d",
  "date_created": "2026-03-02T18:02:31.104000Z",
  "date_modified": "2026-03-02T18:02:31.104000Z",
  "file_hash": "f9ee86687f68bdb8922e068377a457f0a576ab23f4653771615ad3e2ee83e032",
  "private": false,
  "record": {
    "abstract": "We consider a class of two-prover interactive proof systems where each prover\nreturns a single bit to the verifier and the verifier\u0027s verdict is a function\nof the XOR of the two bits received. We show that, when the provers are allowed\nto coordinate their behavior using a shared entangled quantum state, a perfect\nparallel repetition theorem holds in the following sense. The prover\u0027s optimal\nsuccess probability for simultaneously playing a collection of XOR proof\nsystems is exactly the product of the individual optimal success probabilities.\nThis property is remarkable in view of the fact that, in the classical case\n(where the provers can only utilize classical information), it does not hold.\nThe theorem is proved by analyzing parities of XOR proof systems using\nsemidefinite programming techniques, which we then relate to parallel\nrepetitions of XOR games via Fourier analysis.",
    "arxiv_id": "quant-ph/0608146",
    "authors": [
      "Richard Cleve",
      "William Slofstra",
      "Falk Unger",
      "Sarvagya Upadhyay"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Strong Parallel Repetition Theorem for Quantum XOR Proof Systems",
    "url": "https://arxiv.org/abs/quant-ph/0608146"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "317b9c47-0107-4971-80b4-e830c8637ec3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}