A discussion on the origin of quantum probabilities

• Several recent works use a derivation similar to that of R.T. Cox to obtain quantum probabilities.
• We apply Cox’s method to the lattice of subspaces of the Hilbert space.
• We obtain a derivation of quantum probabilities which includes mixed states.
• The method presented in this work is susceptible to generalization.
• It includes quantum mechanics and classical mechanics as particular cases.

We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case).