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, based on the algebraic properties of octonions. Since the protocol does not use any postselection, it can be proven secure against arbitrary collective attacks, by using well-established theorems on the optimality of Gaussian attacks. By using this new coding scheme with an appropriate signal to noise ratio, the distance for secure continuous-variable quantum key distribution can be significantly extended.
Leverrier, A., Alléaume, R., Boutros, J., Zémor, G., & Grangier, P. (2008). Multidimensional reconciliation for continuous-variable quantum key distribution. In IEEE International Symposium on Information Theory - Proceedings (pp. 1020–1024). https://doi.org/10.1109/ISIT.2008.4595141