Unstructured High-Dimensional Time-Phase QKD

Abstract

Conventional QKD systems require generation and detection of quantum states in two different bases, one of which is used to generate a secret key and the other is used to monitor the presence of an eavesdropper. The quantum states can be prepared in any d-dimensional Hilbert space, which means a two-basis QKD system requires generation and detection of d quantum states in the monitoring basis. Recently, Tamaki et al. (Phys Rev A 90:052314, 2014) showed that, for a qubit-based (d = 2) QKD system, the protocol can be secured by transmitting two states in the information basis and only one state in the monitoring basis, while maintaining the same error tolerance against a general coherent attack as a complete setup. Here, I extend this result beyond d = 2 to a generic family of d-dimensional QKD protocols and show that such a system can be secured by transmitting only one state in the monitoring basis. As examples, I apply these findings to investigate the d = 4 time-phase QKD system demonstrated in Chap. 3 and to a d = 7 QKD system realized using the spatial modes of a photon (Mirhosseini et al., New J Phys 17:033033, 2015), illustrating the applicability of this technique to various QKD schemes (Islam et al., Phys Rev A 97:042347, 2018).