Related papers: Classical and Quantum Probabilities as Truth Value…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…
Kolmogorov's foundation of probability takes measure spaces, $\sigma$-algebras, and probability measures as basic objects. It is, however, widely recognized that this classical framework is inadequate for random phenomena involving quantum…
Based on a geometric picture, the example of free particle motion for both classical and quantum domains is considered in the tomographic probability representation. Wave functions and density operators as well as optical and symplectic…
The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved…
Entropic arguments are shown to play a central role in the foundations of quantum theory. We prove that probabilities are given by the modulus squared of wave functions, and that the time evolution of states is linear and also unitary.
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,…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is…
In non-relativistic as well as in special relativistic quantum theory, {\em mass} and {\em charge} are {\em pure numbers} appearing in various (quantum) operators and admit {\em any values}, {\it ie}, values for these quantities are to be…
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for…
Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false, true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the typical…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
Anhomomorphic logic is a new interpretation of Quantum Theory (due to R. Sorkin). It is a histories formulation (c.f. consistent histories, quantum measure theory). In this approach, reality is a co-event, which is essentially an assignment…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
Quantum measurement is commonly posed as a dynamical tension between linear Schr\"odinger evolution and an ad hoc collapse rule. I argue that the deeper conflict is logical: quantum theory is inherently contextual, whereas the classical…