Phase-Aware Multidimensional Reconciliation for Continuous-Variable Quantum Key Distribution

Continuous-variable quantum key distribution (CV-QKD) relies on efficient information reconciliation to establish identical secret key sequences from correlated modulation data and measurement outcomes. Accurate quadrature measurements are essential for reliable reconciliation, but residual phase mismatch between the signal and local oscillator distorts these measurements in coherent receivers and degrades decoding performance. To improve robustness against residual phase mismatch in homodyne-based CV-QKD, we propose a phase-aware multidimensional reconciliation method that jointly performs syndrome-based low-density parity-check (LDPC) decoding and expectation-maximization-based residual-phase refinement. We derive a discrete-time detection model that explicitly incorporates the receiver’s pulse-dependent quadrature-selection phase and construct phase-dependent virtual observations through multidimensional orthogonal mapping. The LDPC decoder provides posterior information for calculating the posterior spherical-symbol moments used in residual-phase refinement, while the refined phase is fed back to update the virtual observations and decoding likelihoods for the next iteration. Numerical results show that the proposed method achieves a lower residual-phase-estimation RMSE than disclosure-based cross-correlation estimation, BER and FER close to those under perfect phase compensation, and a higher finite-size secret key rate.