Related papers: Completely positive classical structures and seque…
This work mainly concerns the -- here introduced -- category of $\mathscr Q$-sets and functional morphisms, where $\mathscr Q$ is a commutative semicartesian quantale. We describe, in detail, the limits and colimits of this complete and…
We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne-Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the so-called effective…
In this paper we investigate operator Hilbert systems and their separable morphisms. We prove that the operator Hilbert space of Pisier is an operator system, which possesses the self-duality property. It is established a link between…
By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalise the traditional quantum-to-classical transition.…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…
We introduce and systematically develop the theory of \emph{quantum doubly stochastic operators}, i.e. positive, trace-preserving maps on non-commutative $L_p$-spaces associated to semifinite von Neumann algebras. After establishing basic…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
We will consider completely positive maps defined on tensor products of von Neumann algebras and taking values in the algebra of bounded operators on a Hilbert space and particularly certain convex subsets of the set of such maps. We show…
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…
Coecke and Heunen described completely positive maps in dagger monoidal categories and the {\sf CP}-infinity construction on these categories in order to construct a category of arbitrary dimensional quantum processes. This article…
The dynamical-algebraic structure underlying all the schemes for quantum information stabilization is argued to be fully contained in the reducibility of the operator algebra describing the interaction with the environment of the coding…
In this paper we introduce and study absolute continuity and singularity of positive operators acting on anti-dual pairs. We establish a general theorem that can be considered as a common generalization of various earlier Lebesgue-type…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
Digital circuits, despite having been studied for nearly a century and used at scale for about half that time, have until recently evaded a fully compositional theoretical in which arbitrary circuits may be freely composed together without…
This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus…
The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and…
Given a locally presentable category together with a suitable functorial cylinder object, we construct model structures which are sensitive to the `direction' of the cylinder. We show that the Covariant and Contravariant model structures on…
In this article we present a new modelling framework for structured concepts using a category-theoretic generalisation of conceptual spaces, and show how the conceptual representations can be learned automatically from data, using two very…
Accurate modeling of decoherence errors in quantum processors is crucial for analyzing and improving gate fidelities. To increase the accuracy beyond that of the Lindblad dynamical map, several generalizations have been proposed, and the…