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, it allows us to express the Markov property for the local structure of the graph. Our main result is the existence and uniqueness of quantum Markov field.
"Construction of a new class of quantum Markov fields." Adv. Oper. Theory 1 (2) 206 - 218, Autumn 2016. https://doi.org/10.22034/aot.1610.1031