Quantum secure direct communication via circle-based two-step quantum walks Yanyan Feng, Sisi Liu, Jian Zhou, Jie Li, Wei Zhao and Jinjing Shi Eur. Phys. J. Plus, 139 8 (2024) 742 Published online: 19 August 2024 DOI: 10.1140/epjp/s13360-024-05557-6