Fig. 3: Phase tracking in the integrated-photonics TF-QKD network using a dual-λ method.

a, Experimental flow chart detailing the initialization, encoding and detection of quantum states. The server-side microcomb and client-side DBR lasers are locked by adjusting injection currents in the gain media. Sequence controls implemented on the QKD client chips are rescaled in the plots with: ➀ IM III, ➁ IM I/II, ➂ PM I, ➃ PM for reference pulse and ➄ output quantum pulse chain. For detection, the server node identifies effective events for quantum signals and performs phase estimation. D_q(r)L(R) denotes the left (L) or right (R) detection outcomes for quantum (q) or reference (r) signals after interference at the server node. b–d, Experimental characterization of phases across the fibre links between those ten pairwise client chips {A_i, B_i}: phases for the reference signals (ϕ_A(B),r) at the wavelength of λ₀ (b); phases for the quantum signals (ϕ_A(B),q) at the wavelength of \({\lambda }_{i}^{{\prime} }\) (c); and their relative phase differences ϕ_d = ((ϕ_B,r − ϕ_A,r) − (ϕ_B,q − ϕ_A,q)) (d). The fibre network used 370-km (185 + 185 km) upstream and predominantly short downstream links, except for the {A₅, B₅} paired QKD, which used 120-km (60 + 60 km) downstream fibres. Phase information was extracted by means of SNSPD-based single-photon interference measurements (10 kHz sampling rate). Data were collected sequentially for each pairwise-linked QKD chips at their wavelength channels, while maintaining continuous operation of all other wavelengths multiplexed in the same fibres (filtered out before injection-locking those microcomb lines of interest). e, An example of phase distributions for the {A₁, B₁} paired QKD chips. Inset, zoom-in view of the initial 100-ms window. f,g, Measured phase drift rate: 2.871 rad ms⁻¹ for ϕ_r and 0.033 rad ms⁻¹ for ϕ_d, through short downstream links {A₁, B₁} (f) and 3.908 rad ms⁻¹ for ϕ_r and 0.069 rad ms⁻¹ for ϕ_d, through long downstream links {A₅, B₅} (g).