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We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…

Quantum Physics · Physics 2026-03-19 P. Arrighi , D. Bakircioglu , N. L. Houyet

We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…

Quantum Physics · Physics 2014-09-01 Erkka Haapasalo , Michal Sedlak , Mario Ziman

Using the technique of quasi difference sets we characterize geometry and automorphisms of configurations which can be presented as a join of some others, in particular - which can be presented as series of cyclically inscribed copies of…

Combinatorics · Mathematics 2012-03-19 Krzysztof Petelczyc , Krzysztof Prażmowski

We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…

Quantum Physics · Physics 2021-01-13 Otto C. W. Kong , Wei-Yin Liu

In this work we consider the task of relaxing the i.i.d assumption in pattern recognition (or classification), aiming to make existing learning algorithms applicable to a wider range of tasks. Pattern recognition is guessing a discrete…

Machine Learning · Computer Science 2012-02-28 Daniil Ryabko

Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…

Quantum Physics · Physics 2015-05-30 L. Derkacz , M. Gwozdz , L. Jakobczyk

In this paper we define and study quasipolar general rings (with or without identity) and extend many of the basic results to the wider class. We obtain some new characterizations of quasipolar and strongly $\pi$-regular elements by using…

Rings and Algebras · Mathematics 2014-11-04 Orhan Gürgün

Semi-supervised learning deals with the problem of how, if possible, to take advantage of a huge amount of not classified data, to perform classification, in situations when, typically, the labelled data are few. Even though this is not…

Statistics Theory · Mathematics 2017-12-18 Alejandro Cholaquidis , Ricardo Fraiman , Mariela Sued

Quantum theory is compatible with scenarios in which the order of operations is indefinite. Experimental investigations of such scenarios, all of which have been based on a process known as the quantum switch, have provided demonstrations…

Quantum Physics · Physics 2023-06-12 Tein van der Lugt , Jonathan Barrett , Giulio Chiribella

Motivated by considerations in the foundations of quantum mechanics and inspired by the literature on vague predicates, we introduce the concept of an opaque predicate. While in the case of vague predicates there is a kind of indeterminacy…

Quantum Physics · Physics 2007-05-23 Decio Krause , Steven French

Here it is shown that standard set theory can be interpreted in a theory about order. The ordering here is about non-extensional flat classes, i.e. classes that are not elements of classes. So, stipulating a nearly well order over all those…

Logic · Mathematics 2023-12-20 Zuhair Al-Johar

We indicate a way of distinguishing between structures, for which, we call two structures distinguishable. Roughly, being distinguishable means that they differ in the number of realizations each gives for some formula. Being…

Logic · Mathematics 2016-11-04 Mohammad Assem

Quantum theory is applicable, in principle, to both the microscopic and macroscopic realms. It is therefore worthwhile to investigate whether it is possible to evolve a quantum-compatible view of the properties and states of macroscopic…

Quantum Physics · Physics 2007-08-14 Ravi Gomatam

The so-called Received View (RV) on quantum non-individuality states, basically, that quantum particles are not individuals. It has received an amount of criticism in the recent literature, most of it concerning the relation between the RV…

History and Philosophy of Physics · Physics 2020-04-29 Décio Krause , Jonas R. B. Arenhart

In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in…

Bell scenarios are multipartite scenarios that exclude any signalling between parties. This leads to a strict hierarchy of classical, quantum, and non-signalling correlations in such scenarios. Here we consider a minimal relaxation of…

Quantum Physics · Physics 2025-07-01 Ravi Kunjwal , Ognyan Oreshkov

Label learning is a fundamental task in machine learning that aims to construct intelligent models using labeled data, encompassing traditional single-label and multi-label classification models. Traditional methods typically rely on…

Machine Learning · Computer Science 2025-11-11 Chenxi Luoa , Zhuangzhuang Zhaoa , Zhaohong Denga , Te Zhangb

Semi-supervised learning deals with the problem of how, if possible, to take advantage of a huge amount of unclassified data, to perform a classification in situations when, typically, there is little labeled data. Even though this is not…

Machine Learning · Statistics 2020-12-11 Alejandro Cholaquidis , Ricardo Fraiman , Mariela Sued

We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…

Probability · Mathematics 2016-02-12 Ehtibar N. Dzhafarov , Janne V. Kujala

Quantum indistinguishability of non-orthogonal quantum states is a valuable resource in quantum information applications such as cryptography and randomness generation. In this article, we present a sequential state-discrimination scheme…

Quantum Physics · Physics 2026-04-28 Lemieux Wang , Hanwool Lee , Joonwoo Bae , Kieran Flatt