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We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
Today it still remains a challenge whether quantum mechanics has an underlying statistical explanation or not. While there are and were a lot of models trying to explain quantum phenomena with statistical methods these all failed on certain…
Quantum decision theory is introduced here, and new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, next on arguments for the Born rule, that is,…
The Heisenberg uncertainty principle is one of the most famous features of quantum mechanics. However, the non-determinism implied by the Heisenberg uncertainty principle --- together with other prominent aspects of quantum mechanics such…
We derive an equation for the current of particles in energy space; particles are subject to a mean field effective potential that may represent quantum effects. From the assumption that non-interacting particles imply a free diffusion…
We consider the Fermi gas in a non-equilibrium state obtained by applying an arbitrary time-dependent potential to the Fermi gas in the ground state. We present a general method that gives the quantum statistics of any single-particle…
We propose a new structure of ensembles in quantum theory, based on the recently introduced intrinsic properties of electrons and photons. On this statistical basis the spreading of a wave-packet, collapse of the wave function, the quantum…
In classical physics the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, unidirectional transfer of population between the densely and sparsely populated…
The exclusion statistics of quasiparticles is found at any level of the hierarchy of condensed states of composite fermion excitations (for which experimental indications have recently been found). The hierarchy of condensed states of…
Quantum experiments yield random data. We show that the most efficient way to store this empirical information by a finite number of bits is by means of the vector of square roots of observed relative frequencies. This vector has the unique…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
Essential elements of quantum theory are derived from an epistemic point of view, i.e., the viewpoint that thetheory has to do with what can be said about nature. This gives a relationship to statistical reasoning and to other areas of…
The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
The quantum state transmission (QST) through the medium of high-dimensional many-particle system is studied with a symmetry analysis. We discover that, if the spectrum matches the symmetry of a fermion or boson system in a certain fashion,…
A quantum microcanonical postulate is proposed as a basis for the equilibrium properties of small quantum systems. Expressions for the corresponding density of states are derived, and are used to establish the existence of phase transitions…
The study of quantum quasi-particles at low temperatures including their statistics, is a frontier area in modern physics. In a seminal paper F.D. Haldane proposed a definition based on a generalization of the Pauli exclusion principle for…
Elementary particles in quantum mechanics (QM) are indistinguishable when sharing the same intrinsic properties and the same quantum state. So, we can consider quantum particles as non-individuals, although non-individuality is usually…
It is a fundamental prediction of quantum theory that states of physical systems are described by complex vectors or density operators on a Hilbert space. However, many experiments admit effective descriptions in terms of other state…
We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield…