Related papers: Computations in Finite Groups and Quantum Physics
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
In this paper we use the recent developments in the representation theory of locally compact quantum groups, to assign, to each locally compact quantum group $\mathbb{G}$, a locally compact group $\tilde \mathbb{G}$ which is the quantum…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
Any real interaction process produces many incompatible system versions, or realisations, giving rise to omnipresent dynamic randomness and universally defined complexity (arXiv:physics/9806002). Since quantum behaviour dynamically emerges…
Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a…
Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very…
The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered…
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…
We will explore the nature of when certain finite groups have an equal covering, and when finite groups do not. Not to be confused with the concept of a cover group, a covering of a group is a collection of proper subgroups whose…