It can be argued that if one can prepare a state x and a different state y , then one can also toss a (possibly biased) coin which lands on one side with probability p and on the other with probability 1 − − p and prepare either x or y , depending on the side the coin lands on. The resulting state is a statistical mixture of the states x and y and in GPTs such statistical mixtures are described by convex combinations, in this case p x + ( 1 − − p ) y . For this reason all state spaces are assumed to be convex sets. Following a similar reasoning, one can argue that also the set of measurement outcomes and set of physical operations must be convex.