Attractors and asymptotic dynamics of open discrete-time quantum walks on cycles

Abstract

Open quantum walks often lead to a classical asymptotic behavior. Here, we look for a simple open quantum walk whose asymptotic behavior can be non-classical. We consider a discrete-time quantum walk on 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.

arXiv comment9 pages, 6 figures, comments welcome

References in corpus (20)

• Quantum entanglement
• Quantum random walks - an introductory overview
• Quantum walks: a comprehensive review
• Quantum Entanglement Growth Under Random Unitary Dynamics
• From quantum cellular automata to quantum lattice gases
• Decoherence in quantum walks - a review
• Open Quantum Random Walks
• Quantum random walks with decoherent coins
• Open Quantum Walks on Graphs
• The structures of state space concerning Quantum Dynamical Semigroups
• Asymptotic dynamics of coined quantum walks on percolation graphs
• Coined quantum walks on percolation graphs
• Quantum Walks
• Asymptotic Evolution of Random Unitary Operations
• Open Quantum Walks: a short introduction
• Microscopic derivation of Open Quantum Walks
• Discrete time quantum walks on percolation graphs
• Percolation induced effects in 2D coined quantum walks: analytic asymptotic solutions
• Properties of Open Quantum Walks on $\mathbb{Z}$
• Asymptotics of quantum Markov processes: From algebraic structure to characterization of asymptotic states