How Interference Effects in Mixtures Determine the Rules of Quantum   Mechanics
  It is shown that elementary indistinguishability properties of partially polarized mixtures are consistent only with the conventional Hilbert space model of quantum mechanics and a few exotic alternatives. This applies even in low dimensions where quantum logic and Gleason's theorem give either weak or no constraints. Experimental methods for eliminating the exotic cases (which include quaternionic and octonionic variants of quantum mechanics) are described. 
Daniel I. Fivel