  We develop a singular layer transmission model for continuous-variable
quantum key distribution (CVQKD). In CVQKD, the transmit information is carried
by continuous-variable (CV) quantum states, particularly by Gaussian random
distributed position and momentum quadratures. The reliable transmission of the
quadrature components over a noisy link is a cornerstone of CVQKD protocols.
The proposed singular layer uses the singular value decomposition of the
Gaussian quantum channel, which yields an additional degree of freedom for the
phase space transmission. This additional degree of freedom can further be
exploited in a multiple-access scenario. The singular layer defines the
eigenchannels of the Gaussian physical link, which can be used for the
simultaneous reliable transmission of multiple user data streams. Our
transmission model also includes the singular interference avoider (SIA)
precoding scheme. The proposed SIA precoding scheme prevents the eigenchannel
interference to reach an optimal transmission over a Gaussian link. We
demonstrate the results through the adaptive multicarrier quadrature
division-multiuser quadrature allocation (AMQD-MQA) CVQKD multiple-access
scheme. We define the singular model of AMQD-MQA and characterize the
properties of the eigenchannel interference. We propose the SIA precoding of
Gaussian random quadratures and the optimal decoding at the receiver. We show a
random phase space constellation scheme for the Gaussian sub-channels. The
singular layer transmission provides improved simultaneous transmission rates
for the users with unconditional security in a multiple-access scenario,
particularly in crucial low signal-to-noise ratio regimes.
