{
  "annotation_id": "b1a00a9a-3d85-4e60-b2e7-2c3fbd5f530e",
  "date_created": "2026-03-02T18:02:13.737000Z",
  "date_modified": "2026-03-02T18:02:13.737000Z",
  "file_hash": "c1967618a5859553e45be8f3ff097a3899388f743666d6e72b1d88fce69427c1",
  "private": false,
  "record": {
    "abstract": "We derive lower bounds for tradeoffs between the communication C and space S\nfor communicating circuits. The first such bound applies to quantum circuits.\nIf for any function f with image Z the multicolor discrepancy of the\ncommunication matrix of f is 1/2^d, then any bounded error quantum protocol\nwith space S, in which Alice receives some l inputs, Bob r inputs, and they\ncompute f(x_i,y_j) for the lr pairs of inputs (x_i,y_j) needs communication\nC=\\Omega(lrd \\log |Z|/S). In particular, n\\times n-matrix multiplication over a\nfinite field F requires C=\\Theta(n^3\\log^2 |F|/S). We then turn to randomized\nbounded error protocols, and derive the bound C=\\Omega(n^3/S^2) for Boolean\nmatrix multiplication, utilizing a new direct product result for the one-sided\nrectangle lower bound on randomized communication complexity. This implies a\nseparation between quantum and randomized protocols.",
    "arxiv_id": "quant-ph/0412088",
    "authors": [
      "Hartmut Klauck"
    ],
    "categories": [
      "quant-ph",
      "cs.CC"
    ],
    "title": "Quantum and Classical Communication-Space Tradeoffs from Rectangle   Bounds",
    "url": "https://arxiv.org/abs/quant-ph/0412088"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7520d323-c0ed-4d1d-ba91-f5056a9ba598",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}