Security of a High Dimensional Two‐Way Quantum Key Distribution Protocol

Two‐way quantum key distribution (QKD) protocols utilize bi‐directional quantum communication to establish a shared secret key. Due to the increased attack surface, security analyses remain challenging. Here a high‐dimensional variant of the Ping Pong protocol is investigated and an information theoretic security analysis in the finite‐key setting is performed. The main contribution in this work is to show a new proof methodology for two‐way quantum key distribution protocols based on the quantum sampling framework of Bouman and Fehr introduced in 2010 and also sampling‐based entropic uncertainty relations introduced by the authors in 2019. The Ping Pong protocol is only investigated here, but these methods may be broadly applicable to other QKD protocols, especially those relying on two‐way channels. Along the way, some fascinating benefits to high‐dimensional quantum states applied to two‐way quantum communication are also showed.