  Gaussian states, operations, and measurements are central building blocks for
continuous-variable quantum information processing which paves the way for
abundant applications, especially including network-based quantum computation
and communication. To make the most use of the Gaussian processes, it is
required to understand and utilize suitable mathematical tools such as the
symplectic space, symplectic algebra, and Wigner representation. Applying these
mathematical tools to practical quantum scenarios, we developed various schemes
for quantum transduction, interference-based bosonic mode permutation and
bosonic sensing. We demonstrated that generic coupler characterized by Gaussian
unitary process can be transformed into a high-fidelity transducer, assuming
the access to infinite squeezing and adaptive feedforward with homodyne
measurements. To address the practical limitation of finite squeezing, we
explored the interference-based protocols. These protocols let us freely
permute bosonic modes only assuming the access to single-mode Gaussian
operations and multiple uses of a given multi-mode Gaussian process. Thus, such
a scheme not only enables universal decoupling for bosonic systems, which is
useful for suppressing undesired coupling between the system and the
environment, but also faithful bidirectional single-mode quantum transduction.
Moreover, noticing that the Gaussian processes are appropriate theoretical
models for optical sensors, we studied the quantum noise theory for optical
parameter sensing and its potential in providing great measurement precision
enhancement. We also extended the Gaussian theories to discrete variable
systems, with several examples such as quantum (gate) teleportation. All the
analyses originated from the fundamental quantum commutation relations, and
therefore are widely applicable.
