Microscopic derivation of open quantum walks

Recently, a formalism for discrete time open quantum walks was introduced [1]. The formalism suggested is similar to the formalism of quantum Markov chains and rests upon the implementation of appropriate completely positive maps. The formalism of the open quantum random walks (OQW) includes the classical random walk and through a physical realization procedure a connection to the unitary quantum walk can be established. Furthermore, the OQW allows for an unravelling in terms of quantum trajectories. It was shown [2] that open quantum walks can perform universal quantum computation and can be used for quantum state engineering