Strengthening security and noise resistance in one-way quantum key distribution protocols through hypercube-based quantum walks

TL;DR

This paper introduces a novel protocol based on QWs over a hypercube topology and demonstrates that, under identical parameters, it provides significantly enhanced security and noise resistance compared to the circular topology, thereby strengthening protection against eavesdropping.

Abstract

Quantum Key Distribution (QKD) is a foundational cryptographic protocol that ensures information-theoretic security. However, classical protocols such as BB84, though favored for their simplicity, offer limited resistance to eavesdropping, and perform poorly under realistic noise conditions. Recent research has explored the use of discrete-time Quantum Walks (QWs) to enhance QKD schemes. In this work, we specifically focus on a one-way QKD protocol, where security depends exclusively on the underlying Quantum Walk (QW) topology, rather than the details of the protocol itself. Our paper introduces a novel protocol based on QWs over a hypercube topology and demonstrates that, under identical parameters, it provides significantly enhanced security and noise resistance compared to the circular topology (i.e., state-of-the-art), thereby strengthening protection against eavesdropping. Furthermore, we introduce an efficient and extensible simulation framework for one-way QKD protocols based on QWs, supporting both circular and hypercube topologies. Implemented with IBM's software development kit for quantum computing (i.e., Qiskit), our toolkit enables noise-aware analysis under realistic noise models. To support reproducibility and future developments, we release our entire simulation framework as open-source. This contribution establishes a foundation for the design of topology-aware QKD protocols that combine enhanced noise tolerance with topologically driven security.

Figures (9)

• Figure 1: Example of a hypercube-based one-way qkd protocol with $P = 2$, $t = 1$, and $N = 1$. When $w_A = 1$, Alice prepares a random initial state $\ket{i_A} = \ket{3} = \ket{11}_2$ from the $2^{P} = 2^2$ set and applies a qw evolution on the hypercube. Bob then inverts the walk and measures in the computational basis to recover $\ket{i_A}$, as highlighted in the second part of the figure. If $w_A = 0$, Alice only prepares $\ket{i_A}$ without any transformation, and Bob directly measures it on a computational basis.
• Figure 2: Minimal security parameter $c$ obtained for each position space dimension $P$ in the circle topology, using $\phi = 0$, $\theta = \pi/4$, and $F = I$. It is important to note that a smaller value of $c$ is more advantageous for Alice and Bob. Additionally, $P$ represents the dimension of the position space. This serves as our state-of-the-art, from which we begin our analysis to improve performance.
• Figure 3: Comparison plot between hypercube and circle-based quantum walks using the same parameters. The minimal value of $c$ for each position space dimension $P$ is shown for both topologies, with $\phi = 0$, $\theta = \pi/4$, and $F = I$. It's important to note that Alice and Bob are better off with a smaller $c$, and $P$ denotes the position space dimension.
• Figure 4: Comparison of the maximally tolerated qer for circle and hypercube-based qkd protocols under depolarizing and amplitude-phase damping noise, using $F = I$, $\phi = 0$, and $\theta = \pi/4$. For $P = 1$, the BB84 limit is recovered, while at $P = 13$, the hypercube-based protocol achieves $Q \approx 0.311$ under depolarizing noise and $Q \approx 0.306$ under amplitude-phase damping, showing improved noise tolerance.
• Figure 5: Comparison of the maximum tolerated qer for circle-based and hypercube-based qkd under different noise types, using optimal parameters from Table \ref{['tab:opt_parameters_combination']}. The hypercube-based protocol shows greater error tolerance: up to $Q \approx 0.361$ (depolarizing) and $Q \approx 0.332$ (amplitude-phase damping).