Coined Quantum Walk on a Quantum Network

Abstract: We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker-moves originates from the unitary interaction of the walker-coin with the qubit degrees of freedom in the quantum network. The walk dynamics leads to a growth of entanglement between the walker and the network on one hand, and on the other, between the network-qubits among themselves. The initial entanglement among the network qubits plays a crucial role in determining the asymptotic values of these entanglement measures and the quantum walk statistics. Specifically, the entanglement entropy of the walker-network state and the negativity of the quantum network-qubit state saturate to values increasing with the initial network-entanglement. The asymptotic time-averaged walker-position probability distribution shows increasing localization around the initial walker-position with higher initial network entanglement. A potential application of these results as a characterisation tool for quantum network properties is suggested.