Related papers: Resource convertibility and ordered commutative mo…

Recently, we have shown that von Neumann algebras form a model for Selinger and Valiron's quantum lambda calculus. In this paper, we explain our choice of interpretation of the duplicability operator "!" by studying those von Neumann…

A notion of convolution is presented in the context of formal power series together with lifting constructions characterising algebras of such series, which usually are quantales. A number of examples underpin the universality of these…

In [arXiv:1006.4939] the enumeration order reducibility is defined on natural numbers. For a c.e. set A, [A] denoted the class of all subsets of natural numbers which are co-order with A. In definition 5 we redefine co-ordering for rational…

Quantum resource theory is perhaps the most revolutionary framework that quantum physics has ever experienced. It plays vigorous roles in unifying the quantification methods of a requisite quantum effect as wells as in identifying protocols…

With the wide range of quantum programming languages on offer now, efficient program verification and type checking for these languages presents a challenge -- especially when classical debugging techniques may affect the states in a…

We construct a resource theory of sharpness for finite-dimensional positive operator-valued measures (POVMs), where the sharpness-non-increasing operations are given by quantum preprocessing channels and convex mixtures with POVMs whose…

In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms" (with Laurent Regnier), we studied a translation of lambda-terms as infinite linear combinations of resource lambda-terms, from a calculus similar to Boudol's…

We investigate the conditions under which an uncontrollable background processes may be harnessed by an agent to perform a task that would otherwise be impossible within their operational framework. This situation can be understood from the…

Units of measure with prefixes and conversion rules are given a formal semantic model in terms of categorial group theory. Basic structures and both natural and contingent semantic operations are defined. Conversion rules are represented as…

We combine the language of monoids with the language of preorders so as to refine some fundamental aspects of the classical theory of factorization and prove an abstract factorization theorem with a variety of applications. In particular,…

The capacity of distant parties to send signals to one another is a fundamental requirement in many information-processing tasks. Such ability is determined by the causal structure connecting the parties, and more generally, by the…

We examine the problem of projecting subsets of a commutative, positively ordered monoid into an $o$-ideal. We prove that to this end one may restrict to a sufficient subset, for whose cardinality we provide an explicit upper bound. Several…

The resource theory of quantum superposition is an extension of the quantum coherent theory, in which linear independence relaxes the requirement of orthogonality. It can be used to quantify the nonclassical in superposition of finite…

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…

Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects…

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…

We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…

Morse projections are well-known in chemistry and allow one, within a Morse potential approximation, to redefine the potential in a simple quadratic form. The latter, being a non-linear transform, is also very helpful for machine learning…

We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded…

While the uptake of data-driven approaches for materials science and chemistry is at an exciting, early stage, to realise the true potential of machine learning models for successful scientific discovery, they must have qualities beyond…