High-order encoding schemes for floodlight quantum key distribution

Floodlight quantum key distribution (FL-QKD) has realized a 1.3 Gbit/s secret-key rate (SKR) over a 10-dB-loss channel against a frequency-domain collective attack [Quantum Sci. Technol. 3, 025007 (2018)2058-956510.1088/2058-9565/aab623]. It achieved this remarkable SKR by means of binary phase-shift keying (BPSK) of multiple optical modes. Moreover, it did so with available technology, and without space-division or wavelength-division multiplexing. In this paper we explore whether replacing FL-QKD's BPSK modulation with a high-order encoding can further increase that protocol's SKR. First, we show that going to K-ary phase-shift keying with K=32 doubles - from 2.0 to 4.5 Gbit/s - the theoretical prediction from [Phys. Rev. A 94, 012322 (2016)2469-992610.1103/PhysRevA.94.012322] for FL-QKD's BPSK SKR on a 50-km-long fiber link. Second, we show that 2d×2d quadrature amplitude modulation does not offer any SKR improvement beyond what its d=1 case - which is equivalent to quadrature phase-shift keying - provides.