Detector Asymmetry in Continuous Variable Quantum Key Distribution

TL;DR

The paper analyzes phase-reference misalignment in LLO-based CV-QKD arising from detector asymmetry in heterodyne measurements and shows how this degrades phase estimation, reducing secure distance and key rate. It introduces a quadrature-symmetrisation post-processing method to compensate for imbalance, supported by experimental data and quantum-state tomography that demonstrate improved state fidelity and lower excess noise. By quantifying misalignment contributions and providing a practical correction, the work offers a path to more robust long-distance CV-QKD with LLOs. This has practical implications for deploying LLO CV-QKD in fiber networks, where detector nonidealities can otherwise limit performance.

Abstract

In Local-local Oscillator (LLO) based Continuous-Variable Quantum Key Distribution (CV-QKD), the phase reference of the transmitter and receiver, Alice and Bob, are naturally de-correlated due to their use of individual lasers. A phase reference signal is used, whose measurement is critical for estimating the phase difference and correcting the raw QKD data. We observed that asymmetry in the quadrature measurements of the shot noise-limited heterodyne detector affects the accuracy of the reference signal's phase estimation and thereby reduces the achievable transmission distance and key rate of the CV-QKD system. We quantify the effect and propose a method to counteract the effect of detection asymmetry. We also evaluate the effects of detection asymmetry using quantum optical tomography.

Figures (7)

• Figure 1: A schematic diagram of a heterodyne detector. A $90$ degree phase shift is applied to one branch of the Local Oscillator (LO), allowing full quadrature reconstruction of the $X$ and $P$ phase space. Blue and green pulses indicate the Gaussian modulated quantum signal and bright LO pulse, respectively.
• Figure 2: A typical polarisation time-multiplexed LLO design. The bottom-left illustration shows the uncertainty in path position between the reference and quantum signals.
• Figure 3: The experimental setup shows a 90 degree optical hybrid, where one arm is attenuated by VOA's to demonstrate different asymmetries. When the power is highly attenuated a larger asymmetry is seen.
• Figure 4: A phase space diagram shows a 14.29$\%$ asymmetry in the raw quadrature data, in orange, and scaled quadrature data, in blue.
• Figure 5: Five experimental results (33.8%---2.3%) of the deviation in phase between the asymmetric data and scaled data, which we model as being the idealised phase (symmetric detector measurement). At every cyclic value of $\pi/4$ we see the largest deviation. A theoretical asymmetry of 50.2% is used for demonstrative purposes to show how in extreme cases the phase deviates significantly from the scaled phase.