  This paper introduces quantum multiparty protocols which allow the use of
temporary assumptions. We prove that secure quantum multiparty computations are
possible if and only if classical multi party computations work. But these
strict assumptions are necessary only during the execution of the protocol and
can be loosened after termination of the protocol.
  We consider two settings:
  1. A collusion of players tries to learn the secret inputs of honest players
or tries to modify the result of the computation.
  2. A collusion of players cheats in the above way or tries to disrupt the
protocol, i.e., the collusion tries to abort the computation or leaks
information to honest players. We give bounds on the collusions tolerable after
a protocol has terminated and we state protocols reaching these bounds.
