dorsal/arxiv
View SchemaMinimum entangled state dimension required for pseudo-telepathy
| Authors | Gilles Brassard, Andre A. Methot, Alain Tapp |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412136 |
| URL | https://arxiv.org/abs/quant-ph/0412136 |
Abstract
Pseudo-telepathy provides an intuitive way of looking at Bell's inequalities, in which it is often obvious that feats achievable by use of quantum entanglement would be classically impossible. A two-player pseudo-telepathy game proceeds as follows: Alice and Bob are individually asked a question and they must provide an answer. They are not allowed any form of communication once the questions are asked, but they may have agreed on a common strategy prior to the execution of the game. We say that they win the game if the questions and answers fulfil a specific relation. A game exhibits pseudo-telepathy if there is a quantum strategy that makes Alice and Bob win the game for all possible questions, provided they share prior entanglement, whereas it would be impossible to win this game systematically in a classical setting. In this paper, we show that any two-player pseudo-telepathy game requires the quantum players to share an entangled quantum system of dimension at least 3x3. This is optimal for two-player games, but the most efficient pseudo-telepathy game possible, in terms of total dimension, involves three players who share a quantum system of dimension 2x2x2.
{
"annotation_id": "826d8cd6-7bce-4c6a-a38a-565b2c9c2d71",
"date_created": "2026-03-02T18:02:12.981000Z",
"date_modified": "2026-03-02T18:02:12.981000Z",
"file_hash": "1324d1a585b49b6ee87a672c2bcbf2af41999be21e20ba4d7d71a04bad747703",
"private": false,
"record": {
"abstract": "Pseudo-telepathy provides an intuitive way of looking at Bell\u0027s inequalities,\nin which it is often obvious that feats achievable by use of quantum\nentanglement would be classically impossible. A two-player pseudo-telepathy\ngame proceeds as follows: Alice and Bob are individually asked a question and\nthey must provide an answer. They are not allowed any form of communication\nonce the questions are asked, but they may have agreed on a common strategy\nprior to the execution of the game. We say that they win the game if the\nquestions and answers fulfil a specific relation. A game exhibits\npseudo-telepathy if there is a quantum strategy that makes Alice and Bob win\nthe game for all possible questions, provided they share prior entanglement,\nwhereas it would be impossible to win this game systematically in a classical\nsetting. In this paper, we show that any two-player pseudo-telepathy game\nrequires the quantum players to share an entangled quantum system of dimension\nat least 3x3. This is optimal for two-player games, but the most efficient\npseudo-telepathy game possible, in terms of total dimension, involves three\nplayers who share a quantum system of dimension 2x2x2.",
"arxiv_id": "quant-ph/0412136",
"authors": [
"Gilles Brassard",
"Andre A. Methot",
"Alain Tapp"
],
"categories": [
"quant-ph"
],
"title": "Minimum entangled state dimension required for pseudo-telepathy",
"url": "https://arxiv.org/abs/quant-ph/0412136"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "8e58efa7-2fa2-4f55-a5cd-6a9412123794",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}