Quantum states of light allow for highly sensitive biosensing configurations, surpassing the limitations imposed by shot-noise. In this theoretical study, we focus on optical plasmonic sensors, which have extensive applications in disease diagnostics, including detection of diseases like HIV. Our investigation involves simulating the impact of quantum states of light, such as the NOON state and squeezed states, on enhancing the limit of detection in a plasmonic phase-sensing biosensor, surpassing coherent light states' shot-noise limit. Specifically, we explore the use of quantum states to improve the limit of detection in phase-based biosensors for HIV detection, operating below the shot-noise limit. Through our analysis, we demonstrate that incorporating quantum states of light in surface plasmon resonance (SPR) biosensing leads to enhanced performance compared to classical states. Moreover, we take into account the impact of environmental losses in the biosensing setup, considering the realworld challenges in practical implementation. Our findings emphasize the potential of quantum SPR biosensors in the development of novel disease diagnostics devices.