  In Discrete Variable Quantum Key Distribution (DV-QKD), homodyne detection
method is frequently employed for its simplicity in use, effectiveness in terms
of error correction, and suitability with contemporary optical communication
systems. Being a coherent detection method, it relies on a local oscillator
whose frequency is matched to that of the transmitted carrier's signal. In this
paper we evaluate a Free Space Optical (FSO) DV-QKD system based on the KMB09
protocol using Homodyne detection under random phase fluctuation and
depolarizing noise error. We present simulation results for System Efficiency
and Quantum Bit Error Rate (QBER) for the proposed model. An obtained
efficiency (approximately 25%) for our proposed DV-QKD system model shows that
under atmospheric turbulence and noise effect, it is inline with the available
analytical results. However, the inclusion of random phase fluctuation and
noise led to higher-than-normal QBER which is anticipated in a real-world
scenario
