Benchmarking Single-Photon Sources for Measurement-Device-Independent Quantum Key Distribution

Abstract

Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) enables secure communication without trusting the measurement devices, but its performance critically depends on the quality of the employed photon sources. We compare MDI-QKD implementations based on Weak Coherent Pulses (WCPs) with those employing Quantum Dot (QD) single-photon sources. WCP-based schemes are fundamentally limited by Poissonian photon-number statistics, imposing a trade-off between single- and multi-photon emissions, whereas QD sources exhibit sub-Poissonian statistics with low antibunching parameter $g^{(2)}(0)$. Using a decoy-state analysis for both source types, we find that even at moderate mean photon numbers, QD-based implementations outperform the best-case WCP configuration - where the mean photon number is optimised at each transmission distance - across the full range of transmission distances. We further incorporate the effect of imperfect photon indistinguishability via Hong-Ou-Mandel interference visibilities into the security framework and demonstrate that both source types are highly sensitive to even small deviations from ideal indistinguishability, significantly affecting achievable key rates and maximum transmission distance.

The paper compares quantum-dot (QD) single-photon sources with weak coherent pulses (WCPs) for polarization-encoded MDI-QKD, asking when sub-Poissonian emission improves key rates and how imperfect photon indistinguishability affects security. It calculates asymptotic decoy-state key rates for symmetric links with identical detector and channel parameters. WCP intensities are optimized at each loss; QD emission is truncated to vacuum, one- and two-photon components, with $g^{(2)}(0)=0.02$. Under perfect indistinguishability, QD sources at nominal brightness $\mu=0.3$ outperform optimized WCPs throughout the transmission range. The crossover brightness is approximately $0.26$ at low loss, decreasing toward $0.2$ at higher loss. A Fock-state interference calculation relates measured Hong–Ou–Mandel visibility to single-photon mode overlap $\gamma$. Existing fidelity and basis-imbalance bounds then translate distinguishability into a phase-error penalty, amplified by inverse single-photon yield. Under the assumed equal pairwise fidelities, even $\gamma=0.999999$ noticeably reduces performance. At $\gamma=0.9999$ and fixed $\mu=0.3$ for both sources, positive key rates extend to approximately $21$ dB for WCPs and $25$ dB for QDs, corresponding to about $25$ km and $40$ km with the chosen efficiencies. The stated limitations include asymptotic rather than finite-size analysis, symmetric channels, identical sources, and fixed antibunching. Remote-QD indistinguishability remains an experimental challenge. Measured visibility also includes apparatus imperfections; using calibrated intrinsic indistinguishability instead would require rigorous justification within the security model.