Fig. 4: QEC performance comparison of the different generalized NP codes.

a Optimized channel infidelity as the function of the mean excitation \({\bar{n}}_{{{{\rm{code}}}}}\) of generalized NP codes which have the same code distance d_N = 4. Here, we choose the error rate γt = 0.5% and κt = 0.1%. The dotted orange line corresponds to the data obtained from Eq. (20), and the break-even line is estimated using Fock states \(\left\vert 0\right\rangle\) and \(\left\vert 1\right\rangle\) for coding. b Optimized SKRPM of generalized NP codes with the fiber coupling loss rate ϵ = 1% and the dephasing error rate Γ_ϕ = 0.1Γ. Here, the y-axis label is the generation rate of secure bits per mode. t₀ is the gate operation time taken for QEC, and 1/t₀ is the raw key generation rate⁸².