A quantum algorithm succeeds not because the superposition principle allows

'the computation of all values of a function at once' via 'quantum

parallelism,' but rather because the structure of a quantum state space allows

new sorts of correlations associated with entanglement, with new possibilities

for information-processing transformations between correlations, that are not

possible in a classical state space. I illustrate this with an elementary

example of a problem for which a quantum algorithm is more efficient than any

classical algorithm. I also introduce the notion of 'pseudo-telepathic' games

and show how the difference between classical and quantum correlations plays a

similar role here for games that can be won by quantum players exploiting

entanglement, but not by classical players whose only allowed common resource

consists of shared strings of random numbers (common causes of the players'

correlated responses in a game).