Coined Quantum Walk on a Quantum Network

TL;DR

This paper investigates how a coined quantum walk on a quantum network creates entanglement and localization effects, influenced by initial network entanglement, with potential applications in characterizing quantum networks.

Contribution

It introduces a model of a coined quantum walk on a quantum network that links initial network entanglement with walk dynamics and entanglement growth, offering new insights.

Findings

Entanglement entropy and negativity saturate to higher values with increased initial network entanglement.

Walker localization around the initial position increases with network entanglement.

Asymptotic walk statistics depend on initial network entanglement levels.

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.