论文标题
图表上的一个正向量子马尔可夫字段
A Forward Quantum Markov Field on Graphs
论文作者
论文摘要
在本文中，我们在图上提出了一类Quantum Markov字段QMF $ g =（v，e）$。考虑到QMF的Markov结构是在基于图形$ g $的基于图形的可观测值的准代数$ \ mathcal {a} _v $的精细结构中研究的。 也就是说，被考虑的马尔可维亚田是通过生成夫妇定义的无限体积状态 $（φ^{（0）}，（\ Mathcal {e} _ {\ {\ {y \} \ cup n_y}））$ n_y} $基于顶点$ y $和它最近的近骨。 本文的主要结果涉及与几个$（φ^{（0）}相关的QMF的独特性，（\ Mathcal {e} _ {\ {\ {y \} \ cup n_y}））$用于包括严格的树木的重要类别。
In this paper, we propose a class of quantum Markov fields QMF on a graphs $G= (V,E)$. The Markov structure of the considered QMF is investigated in the finer structure of a quasi-local algebrav $\mathcal{A}_V$ of observables based over a graphs $G$. Namely, the considered Markovian fields are infinite volume states defined through a generating couple $(φ^{(0)}, (\mathcal{E}_{\{y\}\cup N_y}))$ of a product state $φ^{(0)}$ on $\mathcal{A}_V$ and a family of local transition expectations $\mathcal{E}_{\{y\}\cup N_y}$ based on a vertex $y$ and the set of it nearest-neighbors. The main result of the paper concerns the existence and the uniqueness of QMF associated with a couple $(φ^{(0)}, (\mathcal{E}_{\{y\}\cup N_y}))$ for on an important class of graphs including trees strictly.
