Multidimensional reconciliation for continuous-variable quantum key distribution

We propose a method for extracting an errorless secret key in a continuous-variable quantum key distribution protocol, which is based on Gaussian modulation of coherent states and homodyne detection. The crucial feature is an eight-dimensional reconciliation method, relying on the algebraic properties of octonions. By using this coding scheme with an appropriate signal-to-noise ratio, the distance for secure continuous-variable quantum key distribution can be significantly extended.