Minimum entangled state dimension required for pseudo-telepathy

• Authors: Gilles Brassard;André Allan Méthot;Alain Tapp
• Venue: Quantum Information & Computation
• Year: 2005

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 pseudotelepathy 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 3 × 3. This is optimal for twoplayer games, but the most efficient pseudo-telepathy game possible, in terms of total dimension, involves three players who share a quantum system of dimension 2 × 2 × 2.