Related papers: Symmetric Informationally Complete Measurements Id…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
According to the subjective Bayesian interpretation of quantum theory (QBism), quantum mechanics is a tool that an agent would be wise to use when making bets about natural phenomena. In particular, the Born rule is understood to be a…
The very old problem of the statistical content of quantum mechanics (QM) is studied in a novel framework. The Born's rule (one of the basic postulates of QM) is derived from theory of classical random signals. We present a measurement…
The accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states. Analogously, the informational power quantifies the amount of classical information that can be extracted by…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
The Born rule is part of the collapse axiom in the standard version of quantum theory, as presented by standard textbooks on the subject. We show here that its signature quadratic dependence follows from a single additional physical…
In a Generalised Probabilistic Theory (GPT) equipped additionally with some extra geometric structure we define the morphophoric measurements as those for which the measurement map sending states to distributions of the measurement results…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
Quantum theory has evolved from a set of provisional rules to an indispensable framework that underlies much of modern technology and infrastructure. Yet, after a century, Born's probability postulate remains at odds with the theory's…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
This article summarizes the Quantum Bayesian point of view of quantum mechanics, with special emphasis on the view's outer edges---dubbed QBism. QBism has its roots in personalist Bayesian probability theory, is crucially dependent upon the…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
I. The arena of quantum mechanics and quantum field theory is the abstract, unobserved and unobservable, M-dimensional formal Hilbert space [not equal to] spacetime. II. The arena of observations and, more generally, of all events (i.e.…
Quantum systems can display particle- or wave-like properties, depending on the type of measurement that is performed on them. The Bell-state quantum eraser is an experiment that brings the duality to the forefront, as a single measurement…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope…
We provide a straightforward demonstration of a fundamental difference between classical and quantum mechanics for a single local system; namely the absence of a joint probability distribution of the position $x$ and momentum $p$.…
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…