{
  "annotation_id": "49b1ea22-820a-4733-8f06-31bf4d85f41e",
  "date_created": "2026-03-02T18:01:39.279000Z",
  "date_modified": "2026-03-02T18:01:39.279000Z",
  "file_hash": "335464d68d5b915a94fc5ab442ca441d21c6cecfcf3863573cab0742db8ad6bc",
  "private": false,
  "record": {
    "abstract": "We investigate the power of interaction in two player quantum communication\nprotocols. Our main result is a rounds-communication hierarchy for the pointer\njumping function $f_k$. We show that $f_k$ needs quantum communication\n$\\Omega(n)$ if Bob starts the communication and the number of rounds is limited\nto $k$ (for any constant $k$). Trivially, if Alice starts, $O(k\\log n)$\ncommunication in $k$ rounds suffices. The lower bound employs a result relating\nthe relative von Neumann entropy between density matrices to their trace\ndistance and uses a new measure of information. We also describe a classical\nprobabilistic $k$ round protocol with communication\n$O(n/k\\cdot(\\log^{(k/2)}n+\\log k)+k\\log n)$ in which Bob starts the\ncommunication. Furthermore as a consequence of the lower bound for pointer\njumping we show that any $k$ round quantum protocol for the disjointness\nproblem needs communication $\\Omega(n^{1/k})$ for $k=O(1)$.",
    "arxiv_id": "quant-ph/0004100",
    "authors": [
      "Hartmut Klauck"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On rounds in quantum communication",
    "url": "https://arxiv.org/abs/quant-ph/0004100"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8c5f549b-64cf-4399-83c5-4cd0b93c3bd3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}