{
  "annotation_id": "c840d200-4b2b-400f-9340-96db8f1a1932",
  "date_created": "2026-03-02T18:01:38.354000Z",
  "date_modified": "2026-03-02T18:01:38.354000Z",
  "file_hash": "9b9e5c9be538032fcbf21f9c2f00ecdd9edc7d1d4813afb0ae39076eb8e5ce20",
  "private": false,
  "record": {
    "abstract": "We prove a general lower bound of quantum decision tree complexity in terms\nof some entropy notion. We regard the computation as a communication process in\nwhich the oracle and the computer exchange several rounds of messages, each\nround consisting of O(log(n)) bits. Let E(f) be the Shannon entropy of the\nrandom variable f(X), where X is uniformly random in f\u0027s domain. Our main\nresult is that it takes \\Omega(E(f)) queries to compute any \\emph{total}\nfunction f. It is interesting to contrast this bound with the\n\\Omega(E(f)/log(n)) bound, which is tight for \\emph{partial} functions. Our\napproach is the polynomial method.",
    "arxiv_id": "quant-ph/0008095",
    "authors": [
      "Yaoyun Shi"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Entropy lower bounds of quantum decision tree complexity",
    "url": "https://arxiv.org/abs/quant-ph/0008095"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3987e43c-d168-4377-b58c-b878df805257",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}