Quantum dynamics and entanglement between two discrete-time quantum walkers

We investigate the dynamics and various types of entanglement in a two-particle discrete-time quantum walk with interactions between the walkers. For the case of distinguishable particles, we use the Hubbard model with an internal spin label to describe the hopping and repulsion. Two ways to bipartite the system are considered, one between the spin-up and spin-down and the other between the left and right halves of the space. We contrast the values of the entanglement entropy of these two splittings due to the different ways the subsystems are correlated. Next, we study the entanglement of two identical bosonic quantum walkers via a similar Hamiltonian without any internal spin label. Only the left-right partitions of the space can be investigated by the entanglement entropy in this case. To quantify the entanglement between the two identical particles, we evaluate several correlation functions in the literature and compare them with the case of distinguishable quantum walkers. Our study contrasts different ways to partition a system and entangle the subsystems in multi-particle quantum walks.