Non-additive (fuzzy) measure in quantum mechanics

[@myca9322]

hi! i wonder why you seem to consider the existence of inequivalent decompositions of mixed states as mixtures of pure states to be equivalent to contextuality? there is such a thing as pure state contextuality...

[@AssumptionsofPhysicsResearch]

Right. Allowing multiple decompositions and allowing different context are two different things. But a space of ensemble that allows multiple decomposition is exactly a space that allows different context. This presentation was more geared for people that work on non-additive measure theory, so I didn't really go into that. In classical mechanics, all "pure states" are orthogonal, so you have a single context and single decomposition. This is, for example, the line segment for the single bit case. In quantum mechanics, you can embed multiple classical contexts. For example, in the Bloch ball, every axis in every direction. The center point is in all context (i.e. you can see the maximally mixed state as the mixture (not superposition... really mixture) of any two orthogonal states. You have multiple contexts precisely because the center point can be decomposed in different ways (and consequentely, every other point). So, yes, the pure states all "live" in a different context. But they can do so because at least something else has multiple inequivalent decompositions.

[@myca9322]

@@AssumptionsofPhysicsResearch i at least agree with one direction of the implication: existence of different decompositions implies contextuality. but the other direction doesn't seem accurate. every point on the bloch ball has multiple decompositions-except the pure states which each have exactly one! but, again, contextuality arises even for pure states and projective measurements.