  We prove the secret key rate formulas and derive security threshold
parameters of multicarrier continuous-variable quantum key distribution
(CVQKD). In a multicarrier CVQKD scenario, the Gaussian input quantum states of
the legal parties are granulated into Gaussian subcarrier CVs
(continuous-variables). The multicarrier communication formulates Gaussian
sub-channels from the physical quantum channel, each dedicated to the
transmission of a subcarrier CV. The Gaussian subcarriers are decoded by a
unitary CV operation, which results in the recovered single-carrier Gaussian
CVs. We derive the formulas through the AMQD (adaptive multicarrier quadrature
division) scheme, the SVD-assisted (singular value decomposition) AMQD, and the
multiuser AMQD-MQA (multiuser quadrature allocation). We prove that the
multicarrier CVQKD leads to improved secret key rates and higher tolerable
excess noise in comparison to single-carrier CVQKD. We derive the private
classical capacity of a Gaussian sub-channel and the security parameters of an
optimal Gaussian collective attack in the multicarrier setting. We reveal the
secret key rate formulas for one-way and two-way multicarrier CVQKD protocols,
assuming homodyne and heterodyne measurements and direct and reverse
reconciliation. The results reveal the physical boundaries of physically
allowed Gaussian attacks in a multicarrier CVQKD scenario and confirm that the
improved transmission rates lead to enhanced secret key rates and security
thresholds.
