Related papers: A unified framework for graph algebras and quantum…
Instrumental variables allow the estimation of cause and effect relations even in presence of unobserved latent factors, thus providing a powerful tool for any science wherein causal inference plays an important role. More recently, the…
We provide a general notion of induced structures of operated algebras in the context of unary-binary operads. This notion fully captures the binary quadratic relations encoded by a unary-binary operad, thereby unifying and formalizing the…
Motivated by the theory of Cuntz-Krieger algebras we define and study $ C^\ast $-algebras associated to directed quantum graphs. For classical graphs the $ C^\ast $-algebras obtained this way can be viewed as free analogues of Cuntz-Krieger…
We introduce a new graphical framework for designing quantum error correction codes based on classical principles. A key feature of this graphical language, over previous approaches, is that it is closely related to that of factor graphs or…
In quantum information theory there is a construction for quantum channels, appropriately called a quantum graph, that generalizes the confusability graph construction for classical channels in classical information theory. In this paper,…
k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop the theory of covering spaces for k-graphs, obtaining a…
The study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have never been computed so far. We close this gap by proving that the quantum automorphism group of a finite, directed graph…
In my Montreal lecture notes of 1988, it was suggested that the theory of linear quantum groups can be presented in the framework of the category of {\it quadratic algebras} (imagined as algebras of functions on "quantum linear spaces"),…
Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a…
In this paper, I consider the issue of how two mathematical models of modern physics, the variational principles and the quantum path integral formalism, relate to reality. I assume that the observed phenomena are consistent with the…
Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…
We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be…
We consider a core language of graph queries. These queries are seen as formulas to be solved with respect to graph-oriented databases. For this purpose, we first define a graph query algebra where some operations over graphs and sets of…
The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until…
We define an ultragraph, which is a generalization of a directed graph, and describe how to associate a C*-algebra to it. We show that the class of ultragraph algebras contains the C*-algebras of graphs as well as the Exel-Laca algebras. We…
We argue that the quantum-theoretical structures studied in several recent lines of research cannot be adequately described within the standard framework of quantum circuits. This is in particular the case whenever the combination of…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
Man\v{c}inska and Roberson introduced quantum graph homomorphisms as the existence of perfect quantum strategies for graph homomorphism games. The resulting relation is a quasi-order on finite graphs, and hence gives a partial order after…
The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional…
Partial Boolean algebra underlies the quantum logic as an important tool for quantum contextuality. We propose the notion atom graphs to reveal the graph structure of partial Boolean algebra for finite dimensional quantum systems by proving…