Related papers: Are classical probabilities instances of quantum a…
We review the Consistent Amplitude approach to Quantum Theory and argue that quantum probabilities are explicitly Bayesian. In this approach amplitudes are tools for inference. They codify objective information about how complicated…
I suppose that quantum objects obey elementary probability theory. I consider a connection of elementary probability theory and complex quantum amplitudes by a matrix calculus. A special case of a discrete pregeometry is an example of this…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
This paper addresses the central question of what a coherent concept of probability might look like that would do justice to both classical probability theory, axiomatized by Kolmogorov, and quantum theory. At a time when quanta are…
Classical probability theory is based on assumptions which are often violated in practice. Therefore quantum probability is a proposed alternative not only in quantum physics, but also in other sciences. However, so far it mostly criticizes…
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated…
We show how probabilities can be treated as truth values in suitable sheaf topoi. The scheme developed in this paper is very general and applies to both classical and quantum physics. On the quantum side, the results are a natural extension…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
In this work we initiate the question of whether quantum devices can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it is well…
In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is…
A unifying principle explaining the numerical bounds of quantum correlations remains elusive despite the efforts devoted to identifying it. Here we show that these bounds are indeed not exclusive to quantum theory: for any abstract…
The role of probability in quantum mechanics is reviewed, with a discussion of the ``orthodox'' versus the statistical interpretive frameworks, and of a number of related issues. After a brief summary of sources of unease with quantum…
We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic…
Quantum theory shares with classical probability theory many important properties. I show that this common core regards at least the following six areas, and I provide details on each of these: the logic of propositions, symmetry,…
Classical mechanics is a singular theory in that real-energy classical particles can never enter classically forbidden regions. However, if one regulates classical mechanics by allowing the energy E of a particle to be complex, the particle…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of…
We argue using simple models that all successful practical uses of probabilities originate in quantum fluctuations in the microscopic physical world around us, often propagated to macroscopic scales. Thus we claim there is no physically…