Quantum cryptographic protocols with dual messaging system via 2D alternate quantum walk of a genuine single-photon entangled state

TL;DR

This work addresses secure quantum communication by enabling two distinct messages to be encoded simultaneously in a single-photon quantum walker using a 2D alternate quantum walk (2D AQW). It shows how to generate either genuine three-way single-particle entanglement (SPES) or nonlocal two-way SPES as cryptographic public keys, and provides encryption-decryption procedures based on a unitary evolution $U$ and a commutative shift operator $\hat{T}$, with unconditional security argued via Holevo bounds. The paper also presents explicit experimental avenues for photonic realization, mapping the walker’s degrees of freedom to path, orbital angular momentum, and polarization, and discusses resilience against intercept-and-resend and man-in-the-middle attacks. Compared to prior 1D or non-entangled schemes, this approach achieves dual-message throughput and enhanced security due to richer entanglement structures and the expanded 2D QW evolution space, with potential extensions to even more degrees of freedom. Overall, the results advance quantum cryptography by offering a resource-efficient, high-security framework for simultaneous multi-message transmission using a single photon.

Abstract

A single-photon entangled state (or single-particle entangled state (SPES) in general) can offer a more secure way of encoding and processing quantum information than their multi-photon (or multi-particle) counterparts. The SPES generated via a 2D alternate quantum-walk setup from initially separable states can be either 3-way or 2-way entangled. This letter shows that the generated genuine three-way and nonlocal two-way SPES can be used as cryptographic keys to securely encode two distinct messages simultaneously. We detail the message encryption-decryption steps and show the resilience of the 3-way and 2-way SPES-based cryptographic protocols against eavesdropper attacks like intercept-and-resend and man-in-the-middle. We also detail the experimental realization of these protocols using a single photon, with the three degrees of freedom being OAM, path, and polarization. We have proved that the protocols have unconditional security for quantum communication tasks. The ability to simultaneously encode two distinct messages using the generated SPES showcases the versatility and efficiency of the proposed cryptographic protocol. This capability could significantly improve the throughput of quantum communication systems.

Figures (2)

• Figure 1: (a) $\pi$-tangle $\pi_{xyc}$ vs time steps ($t$) for evolution sequence $M1_xM1_y...$ and with an initially separable state (Eq. (\ref{['eq1']})) with $\phi=\pi$, and $\theta=\frac{\pi}{2}$(best result, dotted red), $\theta=0$(dashed blue), $\theta=\frac{\pi}{8}$(solid cyan). (b) Nonlocal 2-way entanglement negativity $N_{xy}$ vs $t$ for evolution sequence $G1_xG1_y...$ and with the initially separable state with $\phi=\pi$, and $\theta=\frac{\pi}{2}$(best result, dotted red), $\theta=0$(dashed blue), $\theta=\frac{\pi}{8}$(solid cyan).
• Figure 2: Photon-based realization of the quantum cryptography protocol using genuine 3-way single-particle entangled states: (a) the cryptography protocol for secure communication between Bob--Alice--Bob using a photon; (b) Circuit for generation of the public key via AQW using a single photon by Bob and message encryption by Alice; (c) Message Decryption circuit: Bob decrypts the messages from the photon using this circuit. Note that the incoming photon from Alice (blue box) is actually in a superposition of path DoF. Thus, the decryption apparatus (c) is at every probable path of the incoming photon. For instance, at timestep $t=2$ with say message $n=0$ (encrypted in the path DoF), the copies of the decryption apparatus are to be at 3 spatial positions, namely $y=-2$, $y=0$ and $y=2$.