Bridging Classical and Quantum Approaches for Quantitative Sensing of Turbid Media with Polarization-Entangled Photons

Polarimetry with quantum light promises improved measurements for various scenarios. However, fundamental understanding of quantum photonic state transport in complex, real media, and tools to interpret the state after interaction with the sample are still lacking. Here, we theoretically and experimentally explore the evolution of polarization-entangled states in a turbid medium on example of tissue phantoms. By elaborating mathematical relationship between Wolf's coherency matrix and density matrix, we introduce a versatile framework describing the transfer of entangled photons in turbid environments with polarization tracking and resulting quantum state representation with the density operator. Experimentally, we reveal a robust trend in the state evolution depending on the reduced scattering coefficient of the medium. Our theoretical predictions correlate with experimental findings, while the model extends the study by photonic states with different degrees of entanglement. The presented results pave the way for quantitative quantum photonic sensing enabling applications ranging from biomedical diagnostics to remote sensing.