Bridging classical and quantum approaches in optical polarimetry: Predicting polarization-entangled photon behavior in scattering environments

We explore quantum-based optical polarimetry as a potential diagnostic tool for biological tissues by developing a theoretical and experimental framework to understand polarization-entangled photon behavior in scattering media. We investigate the mathematical relationship between Wolf's coherency matrix in classical optics and the density matrix formalism of quantum mechanics which allows for the extension of classical Monte Carlo method to quantum states. The developed generalized Monte Carlo approach uniquely integrates the Bethe-Salpeter equation for classical scattering, the Jones vector formalism for polarization, and the density matrix approach for quantum state representation. Therefore, this unified framework can model both classical and quantum polarization states, handle multi-photon states, and account for varying degrees of entanglement. Additionally, it facilitates the prediction of quantum state evolution in scattering media based on classical optical principles. The validity of the computational model is experimentally confirmed through high-fidelity agreement between predicted and measured quantum state evolution in tissue-mimicking phantoms. This work bridges the gap between classical and quantum optical polarimetry by developing and validating a comprehensive theoretical framework that unifies these traditionally distinct domains, paving the way for future quantum-enhanced diagnostics of tissues and other turbid environments.