Minimum entangled state dimension required for pseudo-telepathy
Minimum entangled state dimension required for pseudo-telepathy
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发表时间：
2004-12
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通讯作者：
G. Brassard;A. A. Méthot-A.;Alain Tapp
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作者：
G. Brassard;A. A. Méthot-A.;Alain Tapp
伪心灵感应提供了一种直观的方式来看待贝尔不等式，在贝尔不等式中，通常很明显，使用量子纠缠实现的壮举在经典上是不可能的。一个两人的伪心灵感应游戏如下进行：爱丽丝和鲍勃分别被问到一个问题，他们必须提供答案。一旦被问到问题，他们就不允许进行任何形式的交流，但他们可能在游戏执行之前就达成了一个共同的策略。我们说，如果问题和答案满足特定的关系，他们就赢得了游戏。如果存在一种量子策略，使得爱丽丝和鲍勃在所有可能的问题上都赢得了游戏，那么这个游戏就会表现出伪心灵感应，前提是他们共享先前的纠缠，而在经典环境中，系统地赢得这个游戏是不可能的。在本文中，我们证明了任何两人伪心灵感应游戏都需要量子参与者共享一个维度至少为3 × 3的纠缠量子系统。这对于两人游戏来说是最佳的，但就总维度而言，最有效的伪心灵感应游戏可能涉及三个共享2 × 2 × 2维度量子系统的玩家。
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.