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Copyright 2002

[ April 3rd 2002 ]

Tomb Raider would be a strange game indeed if Lara Croft could be in two places at once, or simultaneously alive and dead. A new quantum computer game, with quantum rules, hints that these possibilities could face gamers of the future. Jiangfeng Du and colleagues at the University of Science and Technology of China in Hefei demonstrate that a quantum game can be unwinnable by either of two players if both play rationally, but that both can win if they use quantum strategies.

The game in question is a notoriously frustrating one. Devised in the 1950s, it is called the Prisoner's Dilemma. It is basically a gamble . Two players - who can't confer -compete by choosing one of two possible strategies. If both players choose strategy A, say, they both get an equally good pay-off. If both choose strategy B, the pay-off is poor for both.

So it would seem sensible for both players to choose strategy A. But if one chooses B when the other chooses A, the former gets an even better pay-off, the latter, nothing. So there is a temptation to choose B in the hope that the other will choose A. In short, the players could cooperate for a mutually good result, or one of them could defect in the hope of doing even better at the other's expense. Logically, it is always best for both players to select strategy B. That way, they do as well as they can in the face of either of the opponent's choices. But if both players choose B they end up with a pay-off lower than the one they'd get if they both chose A.

This unappealing outcome of mutual defection is known as the Nash equilibrium, after the mathematician John Nash (the subject of the movie A Beautiful Mind). He was the first to show that games like this create inevitable, stable outcomes if played logically. In this classical form of the game, players have a stark choice: to cooperate or to defect. But if the game is played with quantum rules, there are other options: players can choose mixtures of strategies - partly A and partly B. And the mixtures open to the players are interdependent - their choices are said to be entangled.

The amount of strategy mixing allowed depends on the amount of entanglement between players' choices. In a sense, entanglement is a measure of how much quantumness the rules permit. For complete entanglement, a new Nash equilibrium appears in which both players get the good mutual cooperation pay-off. In other words, rational players can fare better than they can in the classical Prisoner's Dilemma. Du and colleagues show that, as the amount of entanglement increases from zero, the game switches twice. First, instead of both players doing equally poorly, one does better than the other. Increasing the entanglement still further produces another switch to the fully quantum game in which both players do equally well.

The quantum computer on which the researchers see these predicted switches of outcome with increasing entanglement is a far cry from a Gameboy. It is an organic molecule in which radio waves can switch the nuclei in a pair of atoms between different states. Different nuclear states represent the strategies of the two players, and under certain conditions these can be entangled. The interaction between the nuclei produces a signal which is a measure of the pay-off that different atomic configurations generate.

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