Entangled Quantum Walkers for Secure Quantum Key Distribution

TL;DR

This work introduces a novel QKD framework using two entangled quantum walkers whose extremal-position correlations, established through entanglement swapping and Bell-state measurements, enable secure key distribution. The authors formalize a discrete coined QRW model and extend it to a two-walker system sharing a coin pair $|c_A,c_B\rangle = k_0|00\rangle + k_1|11\rangle$, deriving recursive amplitude relations and a compact post-BSM state that yields exclusive end-corner correlations depending on the Bell outcome. A concrete 2-step QRW example with parameters $\theta=0.635$, $\lambda=0$, and a specific initial coin state achieves an approximate $81\%$ key-generation probability, with a sifted-key fraction $\cos^{4}(\tfrac{\theta}{2})$, illustrating practical feasibility on near-term hardware. Security is enforced through two verification layers: (i) inspecting the coin distribution around $\epsilon_c$ and (ii) matching observed joint-position distributions to the theoretical model, ensuring that only legitimate end-position correlations contribute to the sifted key. The work broadens QKD design space by integrating entangled QRWs as a resource, motivating future exploration of noisy-channel security, CHSH-based tests, experimental implementations, and privacy-preserving post-processing.

Abstract

Quantum Key Distribution (QKD) is an emerging cryptographic method designed for secure key sharing. Its security is theoretically guaranteed by fundamental principles of quantum mechanics, making it a leading candidate for future communication protocols. Quantum Random Walks (QRWs), on the other hand, are quantum processes that exhibit intriguing phenomena such as interference and superposition, enabling the generation of decentralized and asymmetric probability distributions. Inspired by both fields of study, we propose a novel QKD protocol based on two entangled quantum walkers. Our protocol exploits the unique correlations between the walkers at extremal positions of the walk to establish secret keys shared exclusively by the two parties. The security of the protocol is augmented by analyzing the joint probability distributions of the walkers' measured positions and their associated coin states.

Figures (4)

• Figure 1: Entangled walkers Alice and Bob obtain shared secret keys at opposite corners of the joint quantum walk.
• Figure 2: Probability distribution after 20 steps of a discrete coined QRW.
• Figure 3: Joint probability distribution of Alice and Bob's positions, considering all BSM outcomes. The four corners of the distribution correspond to scenarios where key pairs can be generated. Yellow dots denote the shared key value -2, while white dots indicate the key value 2.
• Figure 4: Joint probability distribution of measured positions when the BSM outcome is (a) $\ket{c_A,c_B} = \ket{00}$ and (b) $\ket{c_A,c_B} = \ket{01}$. Empty grid cells indicate zero probability for the corresponding position pair. The parity of the BSM outcome determines the correlation pattern of the two walkers, allowing Alice to infer Bob's key.