Related papers: The Stochastic-Quantum Correspondence
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
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…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
This paper aims to first explain, somewhat more clearly, the Stochastic-Quantum correspondence put forward in by Barandes in 2023. Specifically, the quantum-mechanical bra-ket notation is used, illuminating some results of previous results.…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that…
Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase space distribution functions. The similarities and differences between quantum and…
A generalization of the stochastic wave function method is presented which allows the unravelling of arbitrary linear quantum master equations which are not necessarily in Lindblad form and, moreover, the explicit treatment of memory…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Why does quantum theory need the complex numbers? With a view toward answering this question, this paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This paper then…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
The field of classical stochastic processes forms a major branch of mathematics. They are, of course, also very well studied in biology, chemistry, ecology, geology, finance, physics, and many more fields of natural and social sciences.…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…
We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
We investigate prepare-and-measure scenarios in which a sender and a receiver use entanglement to send quantum information over a channel with limited capacity. We formalise this framework, identify its basic properties and provide…