Figure 6. Ideal performances in QKD.

We plot the secret-key rate (bits per channel use) versus Alice–Bob's distance (km) at the loss rate of 0.2 dB per km. The secret-key capacity of the channel (red line) sets the fundamental rate limit for point-to-point QKD in the presence of loss. Compare this capacity with a previous non-achievable upperbound¹⁸ (dotted line). We then show the maximum rates that are potentially achievable by current protocols, assuming infinitely long keys and ideal conditions, such as unit detector efficiencies, zero dark count rates, zero intrinsic error, unit error correction efficiency, zero excess noise (for CVs) and large modulation (for CVs). In the figure, we see that ideal implementations of CV protocols (purple lines) are not so far from the ultimate limit. In particular, we consider: (i) One-way no-switching protocol⁶³, coinciding with CV-MDI-QKD²⁰,⁶⁴ in the most asymmetric configuration (relay approaching Alice⁶⁵). For high loss , the rate scales as η/ln 4, which is just 1/2 of the capacity. Same scaling for the one-way switching protocol of ref. 13; (ii) Two-way protocol with coherent states and homodyne detection⁶⁶,⁶⁷ which scales as for high loss (thermal noise is needed for two-way to beat one-way QKD⁶⁶). For the DV protocols (dashed lines), we consider: BB84 with single-photon sources⁴ with rate η/2; BB84 with weak coherent pulses and decoy states⁶ with rate η/(2e); and DV-MDI-QKD⁶⁸,⁶⁹ with rate η/(2e²). See Supplementary Note 6 for details on these ideal rates.