Secret Key Rate Limits in Coexisting Classical-Quantum Optical Links

Abstract

Classical-quantum coexistence enables cost-effective transmission of data and quantum signals over the same fiber-optic channel. Nevertheless, weak quantum-key distribution (QKD) signals are susceptible to non-linear interference generated from the classical traffic, primarily spontaneous Raman scattering (SpRS) and four-wave-mixing (FWM), as well as to unfiltered noise. In QKD protocols, increased channel loss and excess noise both reduce the secret key rates (SKRs), as illustrated in this work for the two-state BB84 and Gaussian-modulated coherent-states (GMCS) protocols. In this study, we derive closed-form expressions for evaluating the accumulated interference power from coexisting classical signals in a quantum frequency channel. Our model enables effective design of classical-quantum systems in single-mode fibers (SMFs), capturing the evolution of interference arising from the relevant physical phenomena. We utilize the model to examine frequency allocation in multiband transmission systems, demonstrating that, contrary to common practice of allocating QKD channels in the O-band, increased SKR is achieved by placing quantum channels in the upper E-/lower S-band across the relevant scenarios.

Figures (14)

• Figure 1: Normalized fwm noise versus fiber length for the given numbers of classical channels (color-coded), together with the linearly averaged value, shown with square markers.
• Figure 2: Normalized interference versus fiber length for the different sources (distinguished by markers) in (a) co-propagating and (b) counter-propagating scenarios.
• Figure 3: (a) Refractive index and effective area of the considered fiber. (b) Wavelength dependence of the group-velocity dispersion, non-linear coefficient, and Rayleigh efficiency. (c) sprs efficiency for different pump wavelengths (color-coded). The shaded background regions indicate the transmission bands. From left to right, the colors correspond to the O-, E-, S-, C-, L-, and U-bands.
• Figure 4: (a) Normalized fwm interference as a function of channel spacing for different index-mismatch values (${i^{2}-h^{2}+k^{2}-l^{2}}$). (b) Normalized fwm matching count $C_{\mathrm{FWM}}$ from \ref{['eq:fwmcount']} and the corresponding continuous distribution $f_{\mathrm{FWM}}$ from \ref{['eq:fwmf']}.
• Figure 5: *skr of gmcs for homodyne- and heterodyne-detected schemes as a function of modulation variance. The transmitter and receivers are assumed as ideal, lossless, and noiseless. Channel parameters are $T=-10dB$ and $\xi=10^{-3}$.