  We propose an efficient logical layer-based reconciliation method for
continuous-variable quantum key distribution (CVQKD) to extract binary
information from correlated Gaussian variables. We demonstrate that by
operating on the raw-data level, the noise of the quantum channel can be
corrected in the low-dimensional (scalar) space and the reconciliation can be
extended to arbitrary dimensions. The CVQKD systems allow an unconditionally
secret communication over standard telecommunication networks. To exploit the
real potential of CVQKD a robust reconciliation technique is needed. It is
currently unavailable, which makes it impossible to reach the real performance
of the CVQKD protocols. The reconciliation is a post-processing step separated
from the transmission of quantum states, which is aimed to derive the secret
key from the raw data. The reconciliation process of correlated Gaussian
variables is a complex problem that requires either tomography in the physical
layer that is intractable in a practical scenario, or high-cost calculations in
the multidimensional spherical space with strict dimensional limitations. To
avoid these issues we define the low-dimensional reconciliation. We prove that
the error probability of one-dimensional reconciliation is zero in any
practical CVQKD scenario, and provides unconditional security. The results
allow to significantly improve the currently available key rates and
transmission distances of CVQKD.
