Related papers: Are classical probabilities instances of quantum a…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
Tracing flows of information in our quantum Universe explains why we see the world as classical.
In this paper, we investigate the classicality and quantumness of a quantum ensemble. We define a quantity called classicality to characterize how classical a quantum ensemble is. An ensemble of commuting states that can be manipulated…
Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude are given. The first game is described by the quantum formalism of spin one half system for which two noncommuting observables…
Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the latter always result from an…
We study transformations of conventional (`classical') probabilities induced by context transitions. It is demonstrated that the transition from one complex of conditions to another induces a perturbation of the classical rule for the…
We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.
Angular momentum in classical and quantum mechanics is carried out beyond textbooks frames. We compare angular distribution of particle position with classical probabilistic approach. Addition of angular momenta is also discussed together…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
I tentatively suggest that the superposition principle of quantum mechanics is explicable in a mathematically natural way if it is possible to understand probability amplitudes as complex-valued logarithms. This notion is inspired by the…
We show that the quantum-mechanical probability distribution involving complex probability amplitudes can be derived from three natural conditions imposed on a relativistically invariant probability function describing the motion of a…
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
Classical statistics and Bayesian statistics refer to the frequentist and subjective theories of probability respectively. Von Mises and De Finetti, who authored those conceptualizations, provide interpretations of the probability that…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most…
A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…