Related papers: Measurable functions on charge spaces
Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and…
Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely non-classical phenomenon provides a necessary ingredient in many quantum information tasks…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the…
Some measurements in quantum mechanics disturb each other. This has puzzled physicists since the formulation of the theory, but only in recent decades has the incompatibility of measurements been analyzed in depth and detail, using the…
This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…
This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the…
The use of charge balance functions in heavy-ion collision studies was initially proposed as a probe of delayed hadronization and two-stage quark production in these collisions. It later emerged that general balance functions can also serve…
Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on…
In this paper we characterize spaces of $L^\infty$-functions on a compact Hausdorff space that are invariant under a transitive and continuous group action. This work generalizes the author's 2021 results concerning the specific case of…
Measurement-based quantum computation has emerged from the physics community as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional…
For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the…
A brief discussion is given of measurement within the context of a theory of "beables", e.g. theories of de Broglie, Bohm, Bell, Vink, and also "modal" theories. It is shown that even in an ideal von Neumann measurement of a beable, the…
We answer the question: "on which metric spaces $(M,d)$ are all continuous functions uniformly continuous?" Our characterization theorem improves and generalizes a previous result due to Levine and Saunders, and in particular is applicable…
By taking into account both quantum mechanical and general relativistic effects, I derive an equation that describes some limitations on the measurability of space-time distances. I then discuss possible features of quantum gravity which…
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…
We identify the task of measuring data to quantitatively characterize the composition of machine learning data and datasets. Similar to an object's height, width, and volume, data measurements quantify different attributes of data along…
In this thesis, we consider the properties of measurements in quantum theory and other operational theories. After having introduced the framework of operational theories, we consider a communication scheme based on an experimental…
We focus on measurability and integrability for set valued functions in non-necessarily separable Fr\'echet spaces. We prove some properties concerning the equivalence between different classes of measurable multifunctions. We also provide…
A transfunction is a function which maps between sets of finite measures on measurable spaces. Push-forward operators form one important class of examples of transfunctions and are identified with their respective measurable functions. In…