Related papers: A tossed coin as quantum mechanical object

This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric…

We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…

We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized…

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…

It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…

The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…

Coin flipping is a cryptographic primitive for which strictly better protocols exist if the players are not only allowed to exchange classical, but also quantum messages. During the past few years, several results have appeared which give a…

When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a…

Coin tossing is a cryptographic task in which two parties who do not trust each other aim to generate a common random bit. Using classical communication this is impossible, but non trivial coin tossing is possible using quantum…

States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…

One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known…

Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…

The concept of quantum commutativity with respect to an action or coaction of a given Hopf algebra is used for the algebraic description of a system of particles and their interaction with certain quantum field. Graded commutativity and…

Account of a system may depend on available methods of gaining information. We discuss a simple discrete system whose description is affected by a specific model of measurement and transformations. It is shown that the limited means of…

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…

In the work it is shown that the principles "the objective local theory" and corollaries of the standard quantum mechanics are not in such antagonistic inconsistency as it is usually supposed. In the framework of algebraic approach, the…

After a general introduction, the thesis is divided into four parts. In the first, we discuss the task of coin tossing, principally in order to highlight the effect different physical theories have on security in a straightforward manner,…

Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…

This is the first chapter of a new and unconventional textbook on quantum mechanics and quantum field theory. The chapter introduces standard quantum mechanics by means of a symmetry principle, without reference to classical mechanics. The…

A localised particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it…