A Qualitative Approach to Quantum Probability, Proceedings - Royal Society. Mathematical, physical and engineering sciences
A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. The question arises as to when such an order can be represented by a quantum probability. We introduce a few behaviorally plausible axioms that provide the answer in two cases: pure state and uniform measure. The general problem is answered by using duality-like conditions. The general problem of characterizing the partial orders that admit a quantum representation by behaviorally justified axioms remains open.
Ehud Lehrer, Eran Shmaya
Lehrer, Ehud, and Eran Shmaya. 2006. A Qualitative Approach to Quantum Probability. Proceedings - Royal Society. Mathematical, physical and engineering sciences. 462(2072): 2331-2344.