Maximal coin-position entanglement generation in a quantum walk for the third step and beyond regardless of the initial state

TL;DR

This paper investigates how to generate maximal entanglement between coin and position in a quantum walk beyond the second step, using optimized coin sequences, and demonstrates this experimentally with linear optics.

Contribution

It provides a rigorous method to determine maximal entanglement generation for any step in a quantum walk, regardless of initial state, using specific coin sequences.

Findings

Maximal entanglement can be achieved beyond the second step with optimized coin sequences.

Experimental demonstration of ten-step quantum walk with high-dimensional entanglement.

Faster probability distribution spreading observed with specific coin sequences.

Abstract

We study maximal coin-position entanglement generation via a discrete-time quantum walk, in which the coin operation is randomly selected from one of two coin operators set at each step. We solve maximal entanglement generation as an optimization problem with quantum process fidelity as the cost function. Then we determine the maximal entanglement that can be rigorously generated for any step beyond the second regardless of initial condition with appropriate coin sequences. The simplest coin sequence comprising Hadamard and identity operations is equivalent to the generalized elephant quantum walk, which exhibits an increasingly faster spreading in terms of probability distribution. Experimentally, we demonstrate a ten-step quantum walk driven by such coin sequences with linear optics, and thereby show the desired high-dimensional bipartite entanglement as well as the transport behavior of faster spreading.