  We introduce a scheme for secure multi-party computation utilising the
quantum correlations of entangled states. First we present a scheme for
two-party computation, exploiting the correlations of a
Greenberger-Horne-Zeilinger state to provide, with the help of a third party, a
near-private computation scheme. We then present a variation of this scheme
which is passively secure with threshold t=2, in other words, remaining secure
when pairs of players conspire together provided they faithfully follow the
protocol. We show that this can be generalised to computations of n-party
polynomials of degree 2 with a threshold of n-1. The threshold achieved is
significantly higher than the best known classical threshold, which satisfies
the bound t<n/2.
