  Continuous Variable-Based Quantum Cryptography (CV-QKD) is an emerging field
in quantum information science, offering unprecedented security for
communication protocols by harnessing the principles of quantum mechanics.
However, ocean environments pose unique challenges to quantum communication due
to their distinct properties and characteristics. This work investigates the
impact of turbulence on the transmission of Gaussian light beams used in a
continuous variable-based quantum key distribution system for underwater
quantum communication. The objective is to quantitatively analyze the induced
losses and propose methodologies to mitigate their effects. To achieve this, we
adopt the widely accepted ABCD matrix formalism, which provides a comprehensive
framework for characterizing the propagation of optical beams through different
media. Moreover, a numerical simulation framework is developed to assess the
resulting losses and evaluate the performance of the proposed system. The
implications of these numerical simulation frameworks for the design and
optimization of quantum communication systems for oceanic environments are
thoroughly discussed.
