  We propose the Gaussian quadrature inference (GQI) method for multicarrier
continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD
protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for
information transmission. The GQI framework provides a minimal error estimate
of the quadratures of the CV quantum states from the discrete, measured noisy
subcarrier variables. GQI utilizes the fundamentals of regularization theory
and statistical information processing. We characterize GQI for multicarrier
CVQKD, and define a method for the statistical modeling and processing of noisy
Gaussian subcarrier quadratures. We demonstrate the results through the
adaptive multicarrier quadrature division (AMQD) scheme. We define direct GQI
(DGQI), and prove that it achieves a theoretical minimal magnitude error. We
introduce the terms statistical secret key rate and statistical private
classical information, which quantities are derived purely by the statistical
functions of GQI. We prove the secret key rate formulas for a multiple access
multicarrier CVQKD via the AMQD-MQA (multiuser quadrature allocation) scheme.
The GQI and DGQI frameworks can be established in an arbitrary CVQKD protocol
and measurement setting, and are implementable by standard low-complexity
statistical functions, which is particularly convenient for an experimental
CVQKD scenario.
