Classical image analysis routinely discards structurally meaningful orientation signatures encoded within Fourier phase, which are easily corrupted by local cellular rotation. Although quantum-inspired data processing offers new avenues for complex signal characterization, practical tools for directly extracting gauge-invariant angular correlations without explicit phase reconstruction remain scarce. Here we introduce Quantum Phase Bicoherence (QPBC) spectroscopy, a novel quantum-interferometric framework for capturing gauge-invariant angular order. The method embeds image angular sectors into a nine-qubit entangled state and probes three-body bicoherence via an ancilla, yielding 16 interpretable readout channels. We validate our framework on three independent public multi-modal imaging datasets covering fluorescence (BBBC021), bright-field (BBBC041) and histopathology (PathMNIST). QPBC consistently resolves angular-phase order and discriminates distinct biological phenotypes with high statistical significance. After principal-axis alignment, the optimal probing frequency universally converges, driven by Fourier directional sensitivity; negative-control experiments fully eliminate discriminative capacity, demonstrating frequency tuning acts as an on-off switch. Cross-dataset benchmarks confirm QPBC outperforms conventional Fourier-phase statistics, where inherent inversion symmetry serves as a built-in pipeline self-check. QPBC delivers a universal, classically unachievable quantitative texture observable, establishes interpretable quantum morphometry, and broadens the toolbox for quantum-inspired analysis applicable to diverse multi-modal microscopic measurements.
Classical image analysis routinely discards structurally meaningful orientation signatures encoded within Fourier phase, which are easily corrupted by local cellular rotation. Although quantum-inspired data processing offers new avenues for complex signal characterization, practical tools for directly extracting gauge-invariant angular correlations without explicit phase reconstruction remain scarce. Here we introduce Quantum Phase Bicoherence (QPBC) spectroscopy, a novel quantum-interferometric framework for capturing gauge-invariant angular order. The method embeds image angular sectors into a nine-qubit entangled state and probes three-body bicoherence via an ancilla, yielding 16 interpretable readout channels. We validate our framework on three independent public multi-modal imaging datasets covering fluorescence (BBBC021), bright-field (BBBC041) and histopathology (PathMNIST). QPBC consistently resolves angular-phase order and discriminates distinct biological phenotypes with high statistical significance. After principal-axis alignment, the optimal probing frequency universally converges, driven by Fourier directional sensitivity; negative-control experiments fully eliminate discriminative capacity, demonstrating frequency tuning acts as an on-off switch. Cross-dataset benchmarks confirm QPBC outperforms conventional Fourier-phase statistics, where inherent inversion symmetry serves as a built-in pipeline self-check. QPBC delivers a universal, classically unachievable quantitative texture observable, establishes interpretable quantum morphometry, and broadens the toolbox for quantum-inspired analysis applicable to diverse multi-modal microscopic measurements.
Out-of-time-order correlators (OTOCs) are central probes of quantum scrambling, and their generalizations have recently become key primitives for both benchmarking quantum advantage and learning the structure of Hamiltonians. Yet their behavior has lacked a unified algorithmic interpretation. We show that higher-order OTOCs naturally fit within the framework of quantum signal processing (QSP): each OTOC(k) measures the 2k-th Fourier component of the phase distribution associated with the singular values of a spatially resolved truncated propagator. This explains the contrasting sensitivities of time-ordered correlators (TOCs) and higher-order OTOCs to causal-cone structure and to chaotic, integrable, or localized dynamics. Based on this understanding, we further generalize higher-order OTOCs by polynomial transformation of the singular values of the spatially resolved truncated propagator. The resultant signal allows us to construct frequency-selective filters, which we call \emph{OTOC spectroscopy}. This extends conventional OTOCs into a mode-resolved tool for probing scrambling and spectral structure of quantum many-body dynamics.
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.
The recently proposed "phase-space microscope" (PSM) extends quantum gas microscopes by allowing joint, single-shot measurements of position and momentum. We show that the n-body correlation functions constructed from such phase-space snapshots determine, in principle, all n-body observables of a many-body quantum state. This establishes phase-space imaging as a complete probe of strongly correlated matter, beyond what snapshots of position and momentum can provide---a limitation that goes back to a famous question posed by Pauli. Even without the full reconstruction of the density matrices, the PSM provides valuable insight into the quantum states. We demonstrate this power through several applications: witnessing entanglement hidden from both position and momentum, including between spatially separated collective degrees of freedom; resolving pairing structure across the BEC-BCS crossover, including the phase of the pair wavefunction and the reconstruction of its two-body Wigner function; probing inhomogeneous systems and preformed pairs without long-range order, relevant to the pseudogap phase; extracting the interaction energy in a magnetic field; and measurements of the local Chern marker. Furthermore, we discuss phase imprinting in the matter-wave Fourier plane as an alternative method for probing time-reversal-symmetry-broken phases such as chiral p-wave superconductors. Together, these results establish the PSM as a versatile new tool for exploring fundamental features of quantum many-body phases in strongly correlated quantum matter.
Advances in neuroimaging and genomics have enabled unprecedented insights into the biological underpinnings of neuropsychiatric disorders; however, integrating heterogeneous, high-dimensional datasets remains a significant analytical challenge. This paper explores quantum neuroinformatics for multi-modal brain imaging, focusing on the integration of functional magnetic resonance imaging (fMRI), electroencephalography (EEG), and genomic data to model complex neuropsychiatric phenotypes. By leveraging hybrid quantum–classical machine learning frameworks, the study examines how quantum-enhanced feature mapping, probabilistic modeling, and high-dimensional optimization can improve the fusion and interpretation of multimodal datasets. The analysis evaluates the potential of quantum algorithms to capture nonlinear interactions across neural, temporal, and genetic domains, while also addressing computational and hardware limitations associated with the Noisy Intermediate-Scale Quantum (NISQ) era. The findings suggest that quantum neuroinformatics may offer a novel pathway for advancing precision psychiatry by enabling more accurate phenotypic classification, biomarker discovery, and personalized treatment strategies.
Quantum-optical coherence tomography (QOCT) is an optical sectioning modality based on the quantum interference of entangled photon pairs in the well-known Hong-Ou-Mandel interferometer. Despite its promise, the technique is far from being competitive with current classical OCT devices due to the long required acquisition times, derived from the low photon-pair emission rates. In this work, we, on the one hand, demonstrate a quantum optical coherence microscopy technique, based on full-field QOCT, which employs entangled collinear photon pairs in a Linnik interferometer designed to overcome some of the limitations of previous QOCT implementations, and, on the other hand, test it on representative samples, including glass layers with manufactured transverse patterns and metal-coated biological specimens. In our setup, while the idler photon is collected with a multimode fiber, the signal photon is detected by an intensified charge-coupled device camera, leading to full-field transverse reconstruction through a single-axial acquisition sequence. Interestingly, our setup permits concurrent OCT and QOCT trace acquisition, the former with greater counts and the latter with the benefit of quantum-conferred advantages. We hope that our current results will represent a significant step forward towards the actual applicability of QOCT, e.g., in clinical settings.
Two-photon interference is a cornerstone of quantum optics, enabling imaging, sensing, and precision measurements that surpass classical limits. By harnessing the quantum interference of photon pairs, as demonstrated by the Hong-Ou-Mandel effect, this approach offers superior axial resolution and intrinsic dispersion cancellation, along with strong noise suppression arising from the precise temporal correlations between photons. Building on these principles, we present the theoretical framework and experimental realization of phase-dependent quantum optical coherence tomography (QOCT), a technique that employs phase-modulated two-photon interference for noninvasive morphological analysis of multilayered samples. We demonstrate that introducing controlled phase shifts to photon pairs in a Hong-Ou-Mandel interferometer effectively eliminates artifacts caused by reflections at different sample layers, thereby greatly improving the accuracy and reliability of QOCT measurements. This work advances the fundamental understanding and practical deployment of two-photon interference, overcoming a key limitation in applying QOCT to real-world applications such as biomedical imaging and materials characterization.