  Continuous-variable quantum key distribution (CVQKD) offers the specific
advantage of sharing keys remotely by the use of standard telecom components,
thereby promoting cost-effective and high-performance metropolitan
applications. Nevertheless, the introduction of high-rate spectrum broadening
has pushed CVQKD from a single-mode to a continuous-mode region, resulting in
the adoption of modern digital signal processing (DSP) technologies to recover
quadrature information from continuous-mode quantum states. However, the
security proof of DSP involving multi-point processing is a missing step. Here,
we propose a generalized method of analyzing continuous-mode state processing
by linear DSP via temporal-modes theory. The construction of temporal modes is
key in reducing the security proof to single-mode scenarios. The proposed
practicality oriented security analysis method paves the way for building
classical compatible digital CVQKD.
