Related papers: On a new measure on infinite dimensional unite cub…
Quantum instruments are mathematical devices introduced to describe the conditional state change during a quantum process. They are completely positive map valued measures on measurable spaces. We may also view them as non-commutative…
We show that in finite dimension a quantum measurement with continuous set of outcomes is always equivalent to a continuous random choice of measurements with only finite outcomes.
We review the status of inclusive |Vub| measurements where many new results have become available recently.
Projections of finite dimensional sets and their measures are investigated in infinite-dimensional power measure spaces. The starting point is the known algebraic formula, expressing \ the $y$-projection of a finite-dimensional set $a$ as a…
In [8] we found a class of overlapping asymmetric self-similar measures on the real line, which are generically absolutely continuous with respect to the Lebesgue measure. Here we construct exceptional measures in this class being singular.
We study $n$-dimensional matrices with $\{0,1\}$-entries ($n$-cubes) such that all their $2$-dimensional slices are incidence matrices of symmetric designs. A known construction of these objects obtained from difference sets is generalized…
We construct measure-preserving mappings from the $d$-dimensional unit cube to the $d$-dimensional unit ball and the compact rank one symmetric spaces, namely the $d$-dimensional sphere, the real, complex, and quaternionic projective…
I discuss some of the main interpretations given to explain the indeterministic nature of quantum measurements and show that all has some loopholes in one corner or another. I propose an alternative interpretation based on the notion of…
The quantum state overlap is the textbook measure of the difference between two quantum states. Yet, it is inadequate to compare the complex configurations of many-body systems. The problem is inherited by the widely employed quantum state…
We introduce a generalization for bounded geometry that we call bounded scale measure. We show that bounded scale measure is a coarse invariant unlike bounded geometry. We then show equivalent definitions for spaces with bounded scale…
Incompatible, i.e. non-jointly measurable quantum measurements are a necessary resource for many information processing tasks. It is known that increasing the number of distinct measurements usually enhances the incompatibility of a…
Let $\mu$ be a Borel probability measure associated with an iterated function system consisting of a countably infinite number of contracting similarities and an infinite probability vector. In this paper, we study the quantization…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems. A major benefit of our presentation is a rigorous description of entanglement of formation. In particular,…
Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or…
One way to interpret smoothness of a measure in infinite dimensions is quasi-invariance of the measure under a class of transformations. Usually such settings lack a reference measure such as the Lebesgue or Haar measure, and therefore we…
The purpose of this paper is to give an effective construction for some induced structures on spheres or product of spheres of codimension 1, 2 or 3, respectively, in Euclidean space endowed with an almost product structure.
This paper is the first in a series of three. The main result, Theorem 1.11, gives an explicit description of the ergodic decomposition for infinite Pickrell measures on spaces of infinite complex matrices. The main construction is that of…
An attempt is made to give a heuristic explanation of the distinguished role of measurement in the quantum theory. We question the notion of "naive" reductionism by stressing the difference between an isolated quantum and classical object.…
We address the issue of angular measure, which is a contested issue for the International System of Units (SI). We provide a mathematically rigorous and axiomatic presentation of angular measure that leads to the traditional way of…
Measures play an important role in the characterisation of various function spaces. In this paper, the structure of density measures will be investigated. These are elements of the dual of the space of essentially bounded func- tions. The…