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

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.

13 pages, 6 figures. Comments are welcome

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Cited by in corpus (6)

• Recurrent generation of maximally entangled single particle states via quantum walks on cyclic graphs
• Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator
• Designing three-way entangled and nonlocal two-way entangled single particle states via alternate quantum walks
• Quantum walks with spatiotemporal fractal disorder
• Deterministic generation of hybrid entangled states using quantum walks
• Phase vs coin vs position disorder as a probe for the resilience and revival of single particle entanglement in cyclic quantum walks