Attractors and asymptotic dynamics of open discrete-time quantum walks on cycles
Adam S. Sajna, T. P. Polak, Antoni Wójcik, Paweł Kurzyński · Physical Review A · 2019
Open quantum walks often lead to a classical asymptotic behavior. Here we look for a simple open quantum walk whose asymptotic behavior can be nonclassical. We consider a discrete-time quantum walk on an $n$-cycle subject to a random coin-dependent phase shift at a single position. This finite system, whose evolution is described by only two Kraus operators, can exhibit all kinds of asymptotic behavior observable in quantum Markov chains: It either evolves towards a maximally mixed state, or partially mixed state, or tends to an oscillatory motion on an asymptotic orbit. We find that the asymptotic orbits do not have a product structure; therefore, the corresponding states can manifest entanglement between the position and the coin degrees of freedom, even if the system started in a product state.