Related papers: Explicit measures for the homogeneous transform

In this mainly pedagogical article, we discuss under what circumstances measurements play a special role in quantum processes. In particular we discuss the following facts which appear to be a common area of confusion: i) from a fundamental…

The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…

We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…

A pedagogical and reasonably self-contained introduction to the measurement problems in quantum mechanics and their partial solution by environment-induced decoherence (plus some other important aspects of dcoherence) is given. The point…

Consistency, defined as the requirement that a series of measurements of the same project carried out by different raters using the same method should produce similar results, is one of the most important aspects to be taken into account in…

This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…

The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…

Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…

We introduce an operational and statistically meaningful measure, the quantum tomographic transfer function, that possesses important physical invariance properties for judging whether a given informationally complete quantum measurement…

Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…

Coherence and correlations represent two related properties of a compound system. The system can be, for instance, the polarization of a photon, which forms part of a polarization-entangled two-photon state, or the spatial shape of a…

We summarise different aspects of the measurement problem in quantum mechanics. We argue that it is a real problem which requires a solution, and identify the properties a theory needs to solve the problem. We show that no current…

The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…

This paper provides unified calculations regarding certain measures and transformations in interacting particle systems. More specifically, we provide certain general conditions under which an interacting particle system will have a…

Roughly speaking, holonomic measures are parametric varifolds without boundary. They provide a setting appropriate for the analysis of many variational problems. In this paper, we characterize the space of variations for these objects, and…

Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…

Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…

Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…

In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…

We study the extent to which the outcomes of a quantum measurement can be manipulated by changing the state of the measurement apparatus. The measurement process is modeled as decoherence induced by the experimenter, to gain knowledge about…