Related papers: One simple postulate implies that every polytopic …
In this paper, 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, is presented and the guidelines to how to extend…
What singles out quantum mechanics as the fundamental theory of Nature? Here we study local measurements in generalised probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We…
We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. A wide…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
Superposition is the core feature that sets quantum theory apart from classical physics. Here, we investigate whether sets of quantum measurements can be modelled by using only devices that are operationally classical, in the sense that…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the…
In this paper we derive the complex Hilbert space formalism of quantum theory from four simple information theoretic axioms. It is shown that quantum theory is the only non classical probabilistic theory satisfying the following axioms:…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
The computational abilities of theories within the generalised probabilistic theory framework has been the subject of much recent study. Such investigations aim to gain an understanding of the possible connections between physical…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary…
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
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,…
We present a new characterization of quantum theory in terms of simple physical principles that is different from previous ones in two important respects: first, it only refers to properties of single systems without any assumptions on the…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…