Entangled Markov chains

摘要: Motivated by the problem of finding a satisfactory quantum generalization classical random walks, we construct new class Markov chains which are at same time purely generated and uniquely determined corresponding chain. We argue that this construction yields as corollary, solution to constructing analogues walks “entangled” in sense specified paper. The formula giving joint correlations these is obtained from replacing usual matrix multiplication Schur multiplication. connection between entanglement clarified showing limits vector states whose amplitudes, given basis (e.g. computational information), complex square roots probabilities chains. In particular, when restricted projectors on basis, chain reduces one. speak entangled lifting, case, Since particular chains, our general also gives motivated study. view possible applications statistical mechanics too, prove ergodic type an with finite state space (thus excluding walks) completely underlying