Abstract
In this paper we will present a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics,
in any finite outcome space, and give the guidelines to how to extend this work to
infinite dimensional Hilbert spaces. Moreover, this new formulation which we will call
extended operational-probabilistic theories, applies not only to quantum systems, but
also equally well to classical systems, without violating Bell’s theorem, and at the same
time solves the measurement problem. This is why we will see that the question of
why our universe is quantum mechanical rather than classical is misplaced. The only
difference that exists between a classical universe and a quantum mechanical one lies
merely in which observables are compatible and which are not. Besides, this extended
probability theory which we present in this paper shows that it is non-determinacy,
or to be more precise, the non-deterministic description of the universe, that makes
the laws of physics the way they are. In addition, this paper shows us that what used
to be considered as purely classical systems and to be treated that way are in fact
able to be manipulated according to the rules of quantum mechanics –with this new
understanding of these rules- and that there is still a possibility that there might be a
deterministic level from which our universe emerges, which if understood correctly, may
open the door wide to applications in areas such as quantum computing. In addition
to all that, this paper shows that without the use of complex vector spaces, we cannot
have any kind of continuous evolution of the states of any system.
Information processing in generalized probabilistic theories
