Related papers: A unified framework for graph algebras and quantum…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
We establish an operator algebra generalization of Watrous' theorem \cite{watrous2009} on mixing unital quantum channels (completely positive trace-preserving maps) with the completely depolarizing channel, wherein the more general objects…
One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
It is known that the classical framework of causal models is not general enough to allow for causal reasoning about quantum systems. While the framework has been generalized in a variety of different ways to the quantum case, much of this…
We present a categorical framework for relating causal models that represent the same system at different levels of abstraction. We define a causal abstraction as natural transformations between appropriate Markov functors, which concisely…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum…
It is commonly assumed that every quantum system is represented by some algebra of operators. Doubt is cast on this assumption by what appears, at first glance, to be a reasonable candidate for a quantum system that is not naturally…
We discuss the case of histories labelled by a continuous time parameter in the {\em History Projection Operator} consistent-histories quantum theory. We describe how the appropriate representation of the history algebra may be chosen by…
Quantum physics can only make statistical predictions about possible measurement outcomes, and these predictions originate from an operator algebra that is fundamentally different from the conventional definition of probability as a…
Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…
We develop an equivariant theory of graphs with respect to quantum symmetries and present a detailed exposition of various examples. We portray unitary tensor categories as a unifying framework encompassing all finite classical simple…
We bring together in one place some of the main results and applications from our recent works in quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time…
To an arbitrary directed graph we associate a row-finite directed graph whose C*-algebra contains the C*-algebra of the original graph as a full corner. This allows us to generalize results for C*-algebras of row-finite graphs to…
We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple…
This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of…
To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…