  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 states which depends on the boundary conditions. Using the provided
construction we investigate QMC associated with XY-model on a Caylay tree of
order two. We prove uniqueness of QMC associated with such a model, this means
the QMC does not depend on the boundary conditions.
