相关论文: Categories of Quantum and Classical Channels (exte…
The paper introduces a (universal) C*-algebra of continuous functions vanishing at infinity on the n-dimensional quantum complex space. To this end, the well-behaved Hilbert space representations of the defining relations are classified.…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
Mixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two 'roads to classicality' coincide. This is…
We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. The foundation is based on distributive monoidal categories. First, we prove that the category of all…
In this paper, we begin by presenting a construction for induced representations of Hilbert modules over pro-$C^*$-algebras for a given continuous $^*$-morphism between pro-$C^*$-algebras. Subsequently, we describe the structure of…
In recent work, symmetric dagger-monoidal (SDM) categories have emerged as a convenient categorical formalization of quantum mechanics. The objects represent physical systems, the morphisms physical operations, whereas the tensors describe…
The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory,…
We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…
The complex numbers are an important part of quantum theory, but are difficult to motivate from a theoretical perspective. We describe a simple formal framework for theories of physics, and show that if a theory of physics presented in this…
We give a definition of partition C*-algebras: To any partition of a finite set, we assign algebraic relations for a matrix of generators of a universal C*-algebra. We then prove how certain relations may be deduced from others and we…
The aim of this paper is to present the construction of a general family of C*-algebras which includes, as a special case, the "quantum spacetime algebra" introduced by Doplicher, Fredenhagen and Roberts. It is based on an extension of the…
We propose a definition of a "$C^*$-Eberlein" algebra, which is a weak form of a $C^*$-bialgebra with a sort of "unitary generator". Our definition is motivated to ensure that commutative examples arise exactly from semigroups of…
Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…
An often used model for quantum theory is to associate to every physical system a C*-algebra. From a physical point of view it is unclear why operator algebras would form a good description of nature. In this paper, we find a set of…
The CBH theorem characterises quantum theory within a C*-algebraic framework. Namely, mathematical properties of C*-algebras modelling quantum systems are equivalent to constraints that are information-theoretic in nature: (1)…
We reconstruct finite-dimensional quantum theory from categorical principles. That is, we provide properties ensuring that a given physical theory described by a dagger compact category in which one may `discard' objects is equivalent to a…
This paper introduces quantum circuit $C^*$-algebra net, which provides a connection between $C^*$-algebra nets proposed in classical machine learning and quantum circuits. Using $C^*$-algebra, a generalization of the space of complex…
There exist several graphical languages for quantum information processing, like quantum circuits, ZX-Calculus, ZW-Calculus, etc. Each of these languages forms a dagger-symmetric monoidal category (dagger-SMC) and comes with an…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
The categories of representations of compact quantum groups of automorphisms of certain inclusions of finite dimensional C*-algebras are shown to be isomorphic to the categories of Fuss-Catalan diagrams.