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A new approach to the problem of measurement in quantum mechanics is proposed. In this approach, the process of measurement is described in the Heisenberg picture and divided into two stages. The first stage is to transduce the measured…
Building upon a recent analysis of the measurement process in Hamiltonian mechanics, this article investigates the Bayesian epistemology of classical physics -- the landscape of accessible probability distributions over phase space. I prove…
Some interactions between classical or quantum fields and matter are known to be irreversible processes. Here we associate an entropy to the electromagnetic field from well-known notions of statistical quantum mechanics, in particular the…
Why do quantum evolutions occur and why do they stop at certain points? In classical thermodynamics affinity was introduced to predict in which direction an irreversible process proceeds. In this paper the quantum mechanical counterpart of…
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…
Measurement of a quantum system provides information concerning the state in which it was prepared. In this paper we show how the retrodictive formalism can be used to evaluate the probability associated with any one of a given set of…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…
No consensus seems to exist as to what constitutes a measurement which is still considered somewhat mysterious in many respects in quantum mechanics. At successive stages mathematical theory of measure, metrology and measurement theory…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
Effective classicality of a property of a quantum system can be defined using redundancy of its record in the environment. This allows quantum physics to approximate the situation encountered in the classical world: The information about a…
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…
Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
We introduce ways to measure information storage in quantum systems, using a recently introduced computation-theoretic model that accounts for measurement effects. The first, the quantum excess entropy, quantifies the shared information…
Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…
In the measurement of a continuous observable Q, the pure components of the reduced state do, in general, depend on the initial state. For measurements which attempt to localize the measured system in a certain region R, the localized wave…
This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is offered. Classical physics proceeds from the…
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…