Recurrent generation of maximally entangled single particle states via quantum walks on cyclic graphs

TL;DR

This paper demonstrates how a single quantum coin can generate maximally entangled single-particle states periodically on cyclic graphs, offering a resource-efficient method with potential quantum cryptography applications.

Contribution

It introduces a simple, resource-efficient scheme for recurrent generation of MESPS using a single coin in quantum walks on cyclic graphs, applicable to various graph sizes.

Findings

Recurrent MESPS can be generated on 4 and 8 site cyclic graphs.

The scheme is resource-saving with straightforward experimental implementation.

Potential application in quantum cryptography protocols.

Abstract

Maximally entangled single-particle states (MESPS) are opening new possibilities in quantum technology as they have the potential to encode more information and are robust to decoherence compared to their nonlocal two-particle counterparts. We find that a single coin can generate MESPS at recurrent time steps (periodically) via discrete-time quantum walks on both $4$ and $8$ site cyclic graphs. This scheme is resource-saving with possibly the most straightforward experimental realization since the same coin is applied at each time step. We also show that recurrent MESPS can be generated on any arbitrary $k$ site cyclic graph, $k\in\{3,4,5,8\}$ via effective-single (Identity and arbitrary coin) or two coin evolution sequences. Beyond their use in fundamental research, we propose an application of the generated MESPS in quantum cryptography protocols. MESPS as cryptographic keys can strengthen quantum-secure communication.