TOMB RAIDER VERSUS
QUANTUM GAME
Copyright 2002 www.nature.com
[ 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
payoff. If both choose strategy B, the payoff
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 payoff,
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 payoff 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 payoff. 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 payoff that different atomic configurations
generate.
