# The role of coherence on two-particle quantum walks

## TL;DR

This paper explores how coherence affects two-bosons quantum walks, providing analytical expressions and demonstrating that initial conditions and coherence influence photon correlations and propagation.

## Contribution

It introduces a general analytical formula for two-bosons correlation functions in pure and mixed states and proposes a quantum-walk scheme affected by coherence.

## Key findings

- Correlation functions depend on initial photon distribution and coherence
- Photon average distance is influenced by initial phase and coherence
- Propagation features align with analytical correlation predictions

## Abstract

We investigate the dynamical properties of the two-bosons quantum walk in system with different degrees of coherence, where the effect of the coherence on the two-bosons quantum walk can be naturally introduced. A general analytical expression of the two-bosons correlation function for both pure states and mixed states is given. We propose a possible two-photon quantum-walk scheme with a mixed initial state and find that the two-photon correlation function and the average distance between two photons can be influenced by either the initial photon distribution, or the relative phase, or the degree of coherence. The propagation features of our numerical results can be explained by our analytical two-photon correlation function.