Robust Genuine Multipartite Entanglement in Two Walker Quantum Walks

This paper investigates the dynamics of bipartite and genuine multipartite entanglement (GME) in a two-walker discrete-time quantum walk (DTQW) on a one-dimensional lattice. The study examines how quantum correlations are generated, redistributed, and transported across composite quantum systems. The authors evaluate systems starting from both separable coin-coin states and maximally entangled Bell states, utilizing logarithmic negativity to quantify bipartite entanglement and the generalized geometric measure (GGM) to quantify genuine multipartite entanglement across the four degrees of freedom (two coins and two positions).

The entanglement dynamics depend strongly on whether the lattice operates in an open-boundary or closed-boundary regime. In the open-boundary regime, where the lattice size exceeds the maximum spatial spread of the walkers, quantum correlations redistribute monotonically. The generalized geometric measure rapidly approaches its theoretical maximum value of $1/2$ and stabilizes. Conversely, the closed-boundary regime introduces pronounced oscillatory behavior in the entanglement measures. This oscillation stems from boundary-induced interference and recurrent wave-packet overlap as the walkers wrap around the finite periodic lattice.

A central focus of the work is testing whether the generation of maximal genuine multipartite entanglement depends strictly on fine-tuned initial conditions or represents a generic dynamical feature. In the open-boundary regime, the GGM remains largely insensitive to the choice of the initial Bell state as well as to continuous variations of the local Hadamard coin operator over a broad parameter range. The only exception occurs near the Pauli-$X$ coin operator, where the walk's behavior changes qualitatively. These findings establish open-boundary two-walker discrete-time quantum walks as robust platforms for engineering multipartite quantum correlations for quantum information processing and simulation.