We propose a theoretical polarization tomography scheme within the quantum imaging with undetected photons (QIUP) framework that extracts the Jones matrix elements, describing the sample's polarization response from interference visibilities and phase shifts. By exploiting inherent constraints among the Jones matrix elements based on the assumptions of fully polarized pure states and linear, non-depolarizing components, the method reduces the number of unknowns required for reliable reconstruction. The same interference-based protocol is also demonstrated for a fully generalized Jones matrix, extending the approach to a broader class of polarization responses. This scheme is well suited for polarization-resolved QIUP implementations with minimal measurement requirements and enables non-invasive characterization of complex samples at different probing and detection wavelengths.
We propose a theoretical polarization tomography scheme within the quantum imaging with undetected photons (QIUP) framework that extracts the Jones matrix elements, describing the sample's polarization response from interference visibilities and phase shifts. By exploiting inherent constraints among the Jones matrix elements based on the assumptions of fully polarized pure states and linear, non-depolarizing components, the method reduces the number of unknowns required for reliable reconstruction. The same interference-based protocol is also demonstrated for a fully generalized Jones matrix, extending the approach to a broader class of polarization responses. This scheme is well suited for polarization-resolved QIUP implementations with minimal measurement requirements and enables non-invasive characterization of complex samples at different probing and detection wavelengths.
Two-photon interference is an important effect that is tightly related to the quantum nature of light. Recently, it has been shown that the photon bunching from the Hong-Ou-Mandel (HOM) effect can be used for quantum imaging in which sample properties (reflection/transmission amplitude, phase delay, or polarization) can be characterized at the pixel-by-pixel level. In this work, we perform Jones matrix imaging for an unknown object based on two-photon interference. By using a reference metasurface with panels of known polarization responses in pairwise coincidence measurements, the object's polarization responses at each pixel can be retrieved from the dependence of the coincidence visibility as a function of the reference polarization. The post-selection of coincidence images with specific reference polarization in our approach eliminates the need in switching the incident polarization and thus parallelized optical measurements for Jones matrix characterization. The parallelization in preparing input states, prevalent in any quantum algorithms, is an advantage of adopting two-photon interference in Jones matrix imaging. We believe our work points to the usage of metasurfaces in biological and medical imaging in the quantum optical regime.
Quantum imaging with undetected photons (QIUP) is an active imaging method in which the detected and the probing photons are distinct and can be selected from different spectral regions. This technique holds potential for a wide range of applications affected by the trade-off between illumination wavelength and detection efficiency. The state-of-the-art experimental configurations assess the spectral absorption and phase information of a target solely in a transmissive configuration, which presents a limitation for applications where the target cannot be aligned with optical elements positioned behind it. In this work, we present an experimental configuration for QIUP of a scattering target, aiming to fill the gap in the applicability of the QIUP technique and enabling QIUP to detect remote targets.
The framework of measurement operators plays a fundamental role in extracting information about quantum systems. Recently, techniques based on induced coherence have been developed to access the same information for undetected photons. However, there has been a lack of consistent reformulation of quantum operators for these techniques. In this work, we introduce a set of parameters that quantify the polarization of undetected photons based on measured visibilities. Given their similarity to classical counterparts, we refer to them as visibility Stokes parameters. We apply these parameters and the corresponding quantum operators to the problem of quantum state tomography, thoroughly analyzing the environment of undetected photons and its role in the reconstruction process. Because these parameters provide a more intuitive and consistent understanding of the measurement process, we believe that some established quantum information protocols could be adapted for undetected photons.
Quantum imaging with undetected photons (QIUP) is a promising technique for non-invasive imaging, particularly at wavelengths where detectors are inefficient or unavailable. Recent studies have investigated the role of polarization in QIUP schemes. In this work, we examine whether post-generation optical elements can recover interference when the signal photons are distinguishable in polarization at the source. Specifically, we employ a Mach-Zehnder interferometer after the photon pairs are generated from two nonlinear crystals. Our results indicate that polarization distinguishability at the time of generation leads to a loss of interference that cannot be restored by post-generation optical arrangements. This highlights the fundamental importance of indistinguishability at the source for maintaining coherence in QIUP systems.
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.
Measurements with undetected photons infer properties of a probe beam that is never detected, transferring mid-infrared information onto silicon-friendly wavelengths. Tomography in this paradigm has so far relied on switched settings or scanned phases, referenced across a drift-sensitive campaign; no protocol reads all Jones parameters from one frame. We show that a folded nonlinear interferometer with a diagonally pumped crossed-crystal source performs coherent process tomography of the undetected beam in a single spectrometer frame: it reconstructs all seven parameters of the beam's round-trip Jones matrix, the coherent part of the channel. Birefringent group-delay walk-off, normally a calibration nuisance, acts as a frequency multiplexer: each Jones-matrix element is assigned its own carrier, a spectral fringe period paired with a detector port. Because the multiplexing exploits the down-conversion bandwidth rather than merely tolerating it, a single Fourier transform per detector trace returns all four moduli and all three relative phases across that bandwidth, i.e., the full round-trip Jones spectrum up to a global phase, with no scan or setting change (after a one-time reference frame). Simultaneity makes every relative phase immune to common-mode drift, and a dark carrier, a self-interference term that unitarity forces to vanish, provides a built-in null test. For realistic parameters of a periodically poled KTP source the scheme yields wavelength-resolved mid-infrared polarimetry across 3.5-4.2 microns (~80 spectral points per Jones element) on a silicon camera, extending to depth-resolved Jones matrices, i.e., polarization-sensitive optical coherence tomography with undetected photons. A Fisher-information analysis, the first we are aware of in undetected-photon tomography, sets the precision budget and compares delay multiplexing to sequential protocols at equal photon number.