Relational Quantum Mechanics and Probability. (arXiv:1803.02644v1 [quant-ph])

We present a discussion on the three postulates of Relational Quantum
Mechanics (RQM) and the definition of probability within this framework. The
first two RQM postulates are based on the information that can be extracted
from interaction of different systems, and the third postulate defines the
properties of the probability function. Here we demonstrate that from a
rigorous definition of the conditional probability for the possible outcomes of
different measurements, the third postulate is unnecessary and the Born's rule
naturally emerges from the first two postulates by applying the Gleason's
theorem. We demonstrate in addition that the probability function is uniquely
defined for classical and quantum phenomena. The presence or not of
interference terms is demonstrated to be related to the precise formulation of
the conditional probability where distributive property on its arguments cannot
be taken for granted. In the particular case of Young's slits experiment, the
two possible argument formulations correspond to the possibility or not to
determine the particle passage through a particular path.

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