Quantum direct communication protocol using recurrence in k-cycle quantum walk

TL;DR

This paper introduces a novel quantum direct communication protocol leveraging the recurrence and entanglement properties of $k$-cycle discrete-time quantum walks, realized optically, and analyzes its security and noise resilience.

Contribution

It presents an optical scheme to implement $k$-cycle DTQW and utilizes its recurrence and entanglement for secure quantum communication.

Findings

Protocol effectively uses recurrence for information retrieval.

Security against intercept-resend attacks demonstrated.

Noise effects on recurrence and mutual information quantified.

Abstract

The ability of quantum walks to evolve in a superposition of distinct quantum states has been used as a resource in quantum communication protocols. Under certain settings, the $k$-cycle discrete-time quantum walks\,(DTQW) are known to recur to its initial state after every $t_r$ steps. We first present a scheme to optically realize any $k$-cycle DTQW using $J$-plate, orbital angular momentum\,(OAM) sorters, optical switch, and optical delay line. This entangles the polarization and OAM degrees of freedom\,(DoF) of a single photon. Making use of this recurrence phenomena of $k$-cycle DTQW and the entanglement generated during the evolution, we present a new quantum direct communication protocol. The recurrence and entanglement in $k$-cycle walk are effectively used to retrieve and secure the information, respectively, in the proposed protocol. We investigate the security of the protocol against intercept and resend attack. We also quantify the effect of amplitude damping and depolarizing noises on recurrence and mutual information between polarization and OAM DoF of a single photon.