Related papers: A Forward Quantum Markov Field on Graphs
In the present paper, we propose a new construction of quantum Markov fields on arbitrary connected, infinite, locally finite graphs. The construction is based on a specific tessellation on the considered graph, that allows us to express…
We introduce quantum Markov states (QMS) in a general tree graph $G= (V, E)$, extending the Cayley tree's case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of this paper concerns the…
We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on $C^*$-algebras defined by general graphs. As examples of generalized d-Markov chains, we…
In this paper, we continue the investigation of quantum Markov states (QMS) and define their mean entropies. Such entropies are explicitly computed under certain conditions. The present work takes a huge leap forward at tackling one of the…
This paper is about algebro-geometrical structures on a moduli space $\CM$ of anomaly-free BV QFTs with finite number of inequivalent observables or in a finite superselection sector. We show that $\CM$ has the structure of F-manifold -- a…
The general framework on the non-local Markovian symmetric forms on weighted $l^p$ $(p \in [1, \infty])$ spaces constructed by [A,Kagawa,Yahagi,Y 2020], by restricting the situation where $p =2$, is applied to such measure spaces as the…
We investigate the structure of the Markov states on general Fermion algebras. The situation treated in the present paper covers, beyond the d--Markov states on the CAR algebra on Z (i.e. when there are d--annihilators and creators on each…
We investigate the relationship between one of the classical notions of boundaries for infinite graphs, \emph{graph ends}, and self-adjoint extensions of the minimal Kirchhoff Laplacian on a metric graph. We introduce the notion of…
In the present paper, we propose a refinement for the notion of quantum Markov states (QMS) on trees. A structure theorem for QMS on general trees is proved. We notice that any restriction of QMS in the sense of Ref. \cite{AccFid03} is not…
We introduce a class of so called Markovian marginals, which gives a natural framework for constructing solutions to the quantum marginal problem. We consider a set of marginals that possess a certain internal quantum Markov chain…
In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those…
We study model theoretic properties of valued fields (equipped with a real-valued multiplicative valuation), viewed as metric structures in continuous first order logic. For technical reasons we prefer to consider not the valued field…
Product-form stationary distributions in Markov chains have been a foundational advance and driving force in our understanding of stochastic systems. In this paper, we introduce a new product-form relationship that we call "graph-based…
We construct Nicolai maps for $N=2$ supersymmetric extensions of minisuperspace models. It is shown that Nicolai maps exist for only a very restricted set of states. In the models considered these are the two states corresponding to the…
We give locally finite Markov trees in $L^p$-compact$,$ separable Hilbert$,$ supersymmetric process$:$ $[0,\infty)\!\times\!\mathbb{R}^{\lvert\mathcal{A}^{\otimes m}\rvert}/\mathcal{A}^{\otimes m}$ on quantum ${\rm…
We study scalar quantum field theory on a compact manifold. The free theory is defined in terms of functional integrals. For positive mass it is shown to have the Markov property in the sense of Nelson. This property is used to establish a…
Markov categories have recently emerged as a powerful high-level framework for probability theory and theoretical statistics. Here we study a quantum version of this concept, called involutive Markov categories. These are equivalent to…
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the…