# Generation of hybrid maximally entangled states in a one-dimensional quantum walk

## TL;DR

This paper investigates methods to generate maximally entangled hybrid states in a one-dimensional quantum walk, comparing different walk types and proposing an experimental scheme using photonic orbital angular momentum.

## Contribution

It introduces an optimization approach for generating hybrid entanglement in quantum walks and benchmarks various walk types for entanglement efficiency.

## Key findings

- Optimal quantum walk yields highest entanglement
- Benchmarking shows differences between Hadamard, random, and optimal walks
- Proposes an experimental scheme using photonic orbital angular momentum

## Abstract

We study the generation of hybrid entanglement in a one-dimensional quantum walk. In particular, we explore the preparation of maximally entangled states between position and spin degrees of freedom. We address it as an optimization problem, where the cost function is the Schmidt norm. We then benchmark the algorithm and compare the generation of entanglement between the Hadamard quantum walk, the random quantum walk and the optimal quantum walk. Finally, we discuss an experimental scheme with a photonic quantum walk in the orbital angular momentum of light. The experimental measurement of entanglement can be achieved with quantum state tomography.