Entanglement distribution is fundamental to quantum communication, but its accuracy is degraded by noise-induced non-unitary dynamics. Conventional quantum circuits face inherent limitations in simulating these processes due to their unitary nature. In this study, we develop a digital quantum simulation framework that employs singular value decomposition and Hilbert space expansion to construct non-unitary operators, enabling precise emulation of decoherence noise dynamics in entangled qubit pairs propagating through quantum communication channels. The method probabilistically simulates noise processes through ancilla-register operations while circumventing the unitary constraints of standard quantum circuits. Numerical simulations confirm the efficacy of the proposed quantum algorithm across various noise types, offering a close approximation to theoretical predictions. We further quantitatively analyze the relationship between noise intensity and entanglement degradation using concurrence measures, providing robust guidance for mitigating the impact of noise in entanglement distribution. Our work establishes a practical pathway for simulating non-unitary dynamics in quantum systems and offers critical insights for developing fault-tolerant entanglement distribution protocols.