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arXiv:2411.06134 · Laser & Photonics Review

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

Vira R. Besaga, Ivan V. Lopushenko, Oleksii Sieryi, Alexander V. Bykov, Frank Setzpfandt, Igor V. Meglinski

Published Jan 4, 2026• 3 citations
arXivHTMLPDF

Abstract

ABSTRACT 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.

DOI
10.1002/lpor.202501172

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ABSTRACT 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.
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Conventional polarimetry, including schemes leveraging entangled light, characterizes optical samples through linear transformations of polarization states. We introduce a two-photon probing approach in which both photons of an entangled pair interact with the same depolarizing medium simultaneously. In this regime, the transformation of the two-photon polarization correlations becomes quadratic in the Mueller matrix, enabling access to second-order polarization information beyond conventional polarimetry. We develop a theoretical framework linking the Mueller matrix to the evolution of the two-photon polarization correlation tensor and show that depolarization induces quadratic degradation of entanglement and state purity. Experiments using polarization-entangled photon pairs transmitted through controlled scattering media confirm the predicted response and reveal enhanced sensitivity to polarization scrambling compared with single-photon probing. These results establish two-photon probing as a higher-order quantum polarimetric modality for characterizing polarization channels.
Abstract A nonlocal quantum approach is presented to polarimetry, leveraging the phenomenon of entanglement in photon pairs to enhance the precision in sample property determination. By employing two distinct channels, one containing the sample of interest and the other serving as a reference, the conditions are explored under which the inherent correlation between entangled photons can increase measurement sensitivity. Specifically, the quantum Fisher information (QFI) is calculated and compare the accuracy and sensitivity for the cases of single sample channel versus two channel quantum state tomography measurements. The theoretical results are verified by experimental analysis. The theoretical and experimental framework demonstrates that the nonlocal strategy enables enhanced precision and accuracy in extracting information about sample characteristics more than the local measurements. Depending on the chosen estimators and noise channels present, theoretical and experimental results show that noise‐induced bias decreases the precision for the estimated parameter. Such a quantum‐enhanced nonlocal polarimetry holds promise for advancing diverse fields including material science, biomedical imaging, and remote sensing, via high‐precision measurements through quantum entanglement.
We investigated the preservation of non-local correlations between polarization-entangled photons when one of them traveled through brain tissue slices of different thicknesses. Using down-converted photons at a wavelength of 802 nm minimized the absorption by the tissue. After the light passed through the tissue samples, we performed quantum state tomography to obtain quantitative measures of the entanglement. We found that entanglement is preserved to a surprising degree, and when it degrades, it does so following a particular path in a tangle versus linear-entropy graph. Such a trajectory reveals direct transfer of probability from entangled to mixed state.
In this paper, we have mainly investigated the reconstruction of the polarization states of the incident light which passed through the turbid atmospheric media. Here, a novel polarization retrieve (PR) method is established using a Monte Carlo simulation algorithm, which is proposed to study the influence of particle scattering. The polarization states of the initial field could be retrieved accurately according to the polarization states of the scattered field and the Mueller matrix. In the case of a single homogeneous medium, the mean error of retrieved polarization is close to zero. We have also applied this method to complex atmospheric environments such as random-sized distribution particles and various index of refraction media. By comparison with the existing polarization maintaining method, the results indicate that the PR method is more applicable to disordered media with relatively larger particles. Moreover, the errors of the retrieved degree of polarization are below 0.11%, and the errors of the retrieved angle of polarization are below 0.54% in our mixed media model. So, this work will be very significant for polarizing quantum secure communication in scattering medium over a long-distance scope.
Quantum-enhanced optical sensing leverages correlations and entanglement in multiphoton states to surpass the limitations of classical measurement. However, the widespread deployment of quantum imaging and polarimetry has been hindered by bulky nonlinear crystals, alignment-sensitive free-space optics, and limited control over the spatial and polarization structure of quantum light. This thesis investigates how engineered nanophotonic metasurfaces, together with two-photon probing schemes, can overcome these constraints and enable compact, versatile, and high-performance quantum sensing platforms. The first component of the thesis introduces a metasurface-enabled quantum imaging system based on spatially entangled photon pairs generated from a subwavelength-thick lithium niobate (LiNbO3) nonlinear metasurface. Exploiting nonlocal guided-mode resonances with strong angular dispersion, the system realizes a hybrid imaging protocol that combines quantum ghost imaging with all-optical wavelength-controlled scanning. A theoretical framework linking momentum-space biphoton correlations to image formation is developed, including the effects of pump-beam waist and metasurface quality factor. Numerical simulations and proof-of-principle experiments demonstrate 2D imaging with strong contrast and establish that metasurface-based photon-pair sources can achieve fields of view and resolution-cell counts far beyond what is possible with bulk-crystal SPDC. Building on this platform, the thesis presents the first quantum phase imaging system that integrates metasurfaces for both photon-pair generation and phase-gradient detection. A silicon (Si) metasurface with a near-linear optical transfer function directly maps phase gradients of transparent samples into spatial quantum correlations, eliminating the need for interferometers or long propagation paths. Experiments show that phase gradients up to 25rad/mm can be retrieved with high fidelity, and the system supports switchable operation between amplitude and phase imaging within a significantly more compact scale. The final component of the thesis develops a two-photon probing quantum polarimetry (TPQP) protocol for characterizing scattering media. By combining Monte Carlo modeling of microscopic photon trajectories with Mueller-matrix decomposition and quantum state tomography, the framework links entanglement degradation to macroscopic polarization observables and resolves ambiguities in Mueller-matrix extraction through tailored probe states. Experiments using tissue-mimicking phantoms confirm that TPQP exhibits significantly higher sensitivity to depolarization than one-photon probing, validating its potential for quantum-enhanced polarimetric sensing and imaging. Overall, this thesis advances quantum optical sensing through two distinct but complementary directions. The first two parts demonstrate how engineered metasurfaces enable compact quantum imaging and phase-gradient detection by integrating photon-pair generation and spatial processing within ultrathin nanophotonic structures. Independently, the two-photon probing quantum polarimetry framework, implemented using a conventional BBO-based entangled source, shows how nonlinear two-photon correlations can enhance sensitivity to depolarization and improve Mueller-matrix reconstruction in scattering media. Although realized on different physical platforms, all components of this work exploit quantum correlations to extract amplitude, phase, and polarization information beyond classical approaches, contributing to the development of practical quantum sensing methodologies.