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The success of machine learning algorithms heavily relies on the quality of samples and the accuracy of their corresponding labels. However, building and maintaining large, high-quality datasets is an enormous task. This is especially true for biomedical data and for meta-sets that are compiled from smaller ones, as variations in image quality, labeling, reports, and archiving can lead to errors, inconsistencies, and repeated samples. Here, we show that the uniform manifold approximation and projection (UMAP) algorithm can find these anomalies essentially by forming independent clusters that are distinct from the main (good) data but similar to other points with the same error type. As a representative example, we apply UMAP to discover outliers in the publicly available ChestX-ray14, CheXpert, and MURA datasets. While the results are archival and retrospective and focus on radiological images, the graph-based methods work for any data type and will prove equally beneficial for curation at the time of dataset creation., Comment: Accepted in MICCAI-2024 Workshop on Topology- and Graph-Informed Imaging Informatics (TGI3)

In this paper, we introduce a neighbor embedding framework for manifold alignment. We demonstrate the efficacy of the framework using a manifold-aligned version of the uniform manifold approximation and projection algorithm. We show that our algorithm can learn an aligned manifold that is visually competitive to embedding of the whole dataset., Comment: Accepted at the ICLR 2022 Workshop on Geometrical and Topological Representation Learning

Pixelation occurs in many imaging systems and limits the spatial resolution of the acquired images. This effect is notably present in quantum imaging experiments with correlated photons in which the number of pixels used to detect coincidences is often limited by the sensor technology or the acquisition speed. Here, we introduce a pixel super-resolution technique based on measuring the full spatially-resolved joint probability distribution (JPD) of spatially-entangled photons. Without shifting optical elements or using prior information, our technique increases the pixel resolution of the imaging system by a factor two and enables retrieval of spatial information lost due to undersampling. We demonstrate its use in various quantum imaging protocols using photon pairs, including quantum illumination, entanglement-enabled quantum holography, and in a full-field version of N00N-state quantum holography. The JPD pixel super-resolution technique can benefit any full-field imaging system limited by the sensor spatial resolution, including all already established and future photon-correlation-based quantum imaging schemes, bringing these techniques closer to real-world applications., Comment: 13 pages, 5 figures

Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display global convergence when given clean data. Neural networks have been used to improve algorithm robustness, but efforts to date are sensitive to initial conditions and give inconsistent performance. Here, we combine iterative methods from phase retrieval with image statistics from deep denoisers, via regularization-by-denoising. The resulting methods inherit the advantages of each approach and outperform other noise-robust phase retrieval algorithms. Our work paves the way for hybrid imaging methods that integrate machine-learned constraints in conventional algorithms.

Imaging with quantum states of light promises advantages over classical approaches in terms of resolution, signal-to-noise ratio and sensitivity. However, quantum detectors are particularly sensitive sources of classical noise that can reduce or cancel any quantum advantage in the final result. Without operating in the single-photon counting regime, we experimentally demonstrate distillation of a quantum image from measured data composed of a superposition of both quantum and classical light. We measure the image of an object formed under quantum illumination (correlated photons) that is mixed with another image produced by classical light (uncorrelated photons) with the same spectrum and polarisation and we demonstrate near-perfect separation of the two superimposed images by intensity correlation measurements. This work provides a novel approach to mix and distinguish information carried by quantum and classical light, which may be useful for quantum imaging, communications, and security.

Light shaping facilitates the preparation and detection of optical states and underlies many applications in communications, computing, and imaging. In this Letter, we generalize light shaping to the quantum domain. We show that patterns of phase modulation for classical laser light can also shape higher orders of spatial coherence, allowing deterministic tailoring of high-dimensional quantum entanglement. By modulating spatially entangled photon pairs, we create periodic, topological, and random patterns of quantum illumination, without effect on intensity. We then structure the quantum illumination to simultaneously compensate for entanglement that has been randomized by a scattering medium and to characterize the medium's properties via a quantum measurement of the optical memory effect. The results demonstrate fundamental aspects of spatial coherence and open the field of adaptive quantum optics.

We develop an analytic model that relates intensity correlation measurements performed by an image sensor to the properties of photon pairs illuminating it. Experiments using both an effective single-photon counting (SPC) camera and a linear electron-multiplying charge-coupled device (EMCCD) camera confirm the model.

Single-photon-sensitive cameras can now be used as massively parallel coincidence counters for entangled photon pairs. This enables measurement of biphoton joint probability distributions with orders-of-magnitude greater dimensionality and faster acquisition speeds than traditional raster scanning of point detectors; to date, however, there has been no general formula available to optimize data collection. Here we analyze the dependence of such measurements on count rate, detector noise properties, and threshold levels. We derive expressions for the biphoton joint probability distribution and its signal-to-noise ratio (SNR), valid beyond the low-count regime up to detector saturation. The analysis gives operating parameters for global optimum SNR that may be specified prior to measurement. We find excellent agreement with experimental measurements within the range of validity, and discuss discrepancies with the theoretical model for high thresholds. This work enables optimized measurement of the biphoton joint probability distribution in high-dimensional joint Hilbert spaces., Comment: 9 pages, 5 figures, 1 table

Quantum entangled states of light are essential for quantum technologies and fundamental tests of physics. While quantum information science has relied on systems with entanglement in 2D degrees of freedom, e.g. quantum bits with polarization states, the field is moving towards ever-higher dimensions of entanglement. Increasing the dimensionality enhances the channel capacity and security of quantum communication protocols, gives rise to exponential speed-up of quantum computation, and is necessary for quantum imaging. Yet, characterization of even bipartite quantum states of high-dimensional entanglement remains a prohibitively time-consuming challenge, as the dimensionality of the joint Hilbert space scales quadratically with the number of modes. Here, we develop and experimentally demonstrate a new, more complete theory of detection in CCD cameras for rapid measurement of the full joint probability distribution of high-dimensional quantum states. The theory spans the intensity range from low photon count to saturation of the detector, while the massive parallelization inherent in the pixel array makes measurements scale favorably with dimensionality. The results accurately account for partial detection and electronic noise, resolve the paradox of ignoring two-photon detection in a single pixel despite collinear spatial entanglement, and reveal the full Hilbert space for exploration. For example, use of a megapixel array allows measurement of a joint Hilbert space of 1012 dimensions, with a speed-up of nearly four orders of magnitude over traditional methods. We demonstrate the method with pairs, but it generalizes readily to arbitrary numbers of entangled photons. The technique uses standard geometry with existing technology, thus removing barriers of entry to quantum imaging experiments, and open previously inaccessible regimes of high-dimensional quantum optics., Comment: Article: 5 pages, 3 figures, 1 table. Supplement: 5 pages, 2 figures

Losses should be accounted for in a complete description of quantum imaging systems, and yet they are often treated as undesirable and largely neglected. In conventional quantum imaging, images are built up by coincidence detection of spatially entangled photon pairs (biphotons) transmitted through an object. However, as real objects are non-unitary (absorptive), part of the transmitted state contains only a single photon, which is overlooked in traditional coincidence measurements. The single photon part has a drastically different spatial distribution than the two-photon part. It contains information both about the object, and, remarkably, the spatial entanglement properties of the incident biphotons. We image the one- and two-photon parts of the transmitted state using an electron multiplying CCD array both as a traditional camera and as a massively parallel coincidence counting apparatus, and demonstrate agreement with theoretical predictions. This work may prove useful for photon number imaging and lead to techniques for entanglement characterization that do not require coincidence measurements., Comment: 7 pages, 5 figures

We explore, both experimentally and theoretically, the propagation dynamics of spatially entangled photon pairs (biphotons). Characterization of entanglement is done via the Schmidt number, which is a universal measurement of the degree of entanglement directly related to the non-separability of the state into its subsystems. We develop expressions for the terms of the Schmidt number that depend on the amplitude and phase of the commonly used double-Gaussian approximation for the biphoton wave function, and demonstrate migration of entanglement between amplitude and phase upon propagation. We then extend this analysis to incorporate both phase curvature in the pump beam and higher spatial frequency content of more realistic non-Gaussian wave functions. Specifically, we generalize the classical beam quality parameter M2 to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics., Comment: 7 pages, 4 figures, includes supplementary material

Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial resolution, while common components of noise can be subtracted. Even more, they can accomplish this while physically separate, due to the nonlocal properties of quantum mechanics. Indeed, nearly all quantum optics experiments rely on this separation, using individual point detectors that are scanned to measure coincidence counts and correlations. Scanning, however, is tedious, time consuming, and ill-suited for imaging. Moreover, the separation of beam paths adds complexity to the system while reducing the number of photons available for sampling, and the multiplicity of detectors does not scale well for greater numbers of photons and higher orders of entanglement. We bypass all of these problems here by directly imaging collinear photon pairs with an electron-multiplying CCD camera. We show explicitly the benefits of quantum nonlocality by engineering the spatial entanglement of the illuminating photons and introduce a new method of correlation measurement by converting time-domain coincidence counting into spatial-domain detection of selected pixels. We show that classical transport-of-intensity methods are applicable in the quantum domain and experimentally demonstrate nearly optimal (Heisenberg-limited) phase measurement for the given quantum illumination. The methods show the power of direct imaging and hold much potential for more general types of quantum information processing and control.

Nonlinear imaging systems can surpass the limits of linear optics, but to date they have all relied on physical media (e.g. crystals) to work. These materials are all constrained by their physical properties, such as frequency selectivity, environmental sensitivity, time behavior, and fixed nonlinear response. Here, we show that electro-optic spatial light modulators (SLMs) can take the place of traditional nonlinear media, provided that there is a feedback between the shape of the object and the pattern on the modulator. This feedback creates a designer illumination that generalizes the field of adaptive optics to include object-dependent patterns. Unlike physical media, the SLM response can provide arbitrary mathematical functions, operate over broad bandwidths at high speeds, and work equally well at high power and single-photon levels. We demonstrate the method experimentally for both coherent and incoherent light.

Phase transitions give crucial insight into many-body systems, as crossovers between different regimes of order are determined by the underlying dynamics. These dynamics, in turn, are often constrained by dimensionality and geometry. For example, in one- and two-dimensional systems with continuous symmetry, thermal fluctuations prevent the formation of long-range order[1,2]. Two-dimensional systems are particularly significant, as vortices can form in the plane but cannot tilt out of it. At high temperatures, random motion of these vortices destroys large-scale coherence. At low temperatures, vortices with opposite spin can pair together, cancelling their circulation and allowing quasi-long-range order to appear. This Berezenskii-Kosterlitz-Thouless (BKT) transition[3,4] is essentially classical, arising for example in the traditional XY model for spins, but to date experimental evidence has been obtained only in cold quantum systems. Measurements of superfluid sound speed[5] and critical velocity[6] have been consistent with scaling predictions, and vortices have been observed directly in cold atom experiments[7,8]. However, the presence of trapping potentials restricts measurement to vortex density, rather than number, and obscures the process of vortex unbinding. Further, atom and fluid experiments suffer from parasitic heating and difficulties in phase recording, leading to results that differ from theory in many quantitative aspects. Here, we use a nonlinear optical system to directly observe the ideal BKT transition, including vortex pair dynamics and the correlation properties of the wavefunction, for both repulsive and attractiveinteractions (the photonic equivalent of ferromagnetic and antiferromagnetic conditions[9]). The results confirm the thermodynamics of the BKT transition and expose outstanding issues in the crossovers to superfluidity and Bose-Einstein condensation., Comment: 7 pages, 4 figures

We demonstrate an all-optical bump-on-tail instability by considering the nonlinear interaction of two partially-coherent spatial beams. For weak wave coupling, we observe momentum transfer with no variation in intensity. For strong wave coupling, modulations appear in intensity and evidence appears for wave (Langmuir) collapse at large scales. Borrowing plasma language, these limits represent regimes of weak and strong spatial optical turbulence. In both limits, the internal spectral energy redistribution is observed by recording and reconstructing a hologram of the evolving dynamics. The results are universal and can appear in any wave-kinetic system with short-wave/long-wave coupling.

We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation., Comment: 11 pages, 4 figures 2 added references on p. 4

In most classical fluids, shock waves are strongly dissipative, their energy being quickly lost through viscous damping. But in systems such as cold plasmas, superfluids, and Bose-Einstein condensates, where viscosity is negligible or non-existent, a fundamentally different type of shock wave can emerge whose behaviour is dominated by dispersion rather than dissipation. Dispersive shock waves are difficult to study experimentally, and analytical solutions to the equations that govern them have only been found in one dimension (1D). By exploiting a well-known, but little appreciated, correspondence between the behaviour of superfluids and nonlinear optical materials, we demonstrate an all-optical experimental platform for studying the dynamics of dispersive shock waves. This enables us to observe the propagation and nonlinear response of dispersive shock waves, including the interaction of colliding shock waves, in 1D and 2D. Our system offers a versatile and more accessible means for exploring superfluid-like and related dispersive phenomena., Comment: 21 pages, 6 figures Revised abstract

We demonstrate second-band bright vortex-array solitons in photonic lattices. This constitutes the first experimental observation of higher-band solitons in any 2D periodic system. These solitons possess complex intensity and phase structures, yet they can be excited by a simple highly-localized vortex-ring beam. Finally, we show that the linear diffraction of such beams exhibits preferential transport along the lattice axes.

We present a novel, real-time, experimental technique for linear and nonlinear Brillouin zone spectroscopy of photonic lattices. The method relies on excitation with random-phase waves and far-field visualization of the spatial spectrum of the light exiting the lattice. Our technique facilitates mapping the borders of the extended Brillouin zones and the areas of normal and anomalous dispersion within each zone. For photonic lattices with defects (e.g., photonic crystal fibers), our technique enables far-field visualization of the defect mode overlaid on the extended Brillouin zone structure of the lattice. The technique is general and can be used for photonic crystal fibers as well as for periodic structures in areas beyond optics.

We predict random-phase spatial solitons in instantaneous nonlocal nonlinear media. The key mechanism responsible for self-trapping of such incoherent wave-packets is played by the non-local (rather than the traditional non-instantaneous) nature of the nonlinearity. This new kind of incoherent solitons has profoundly different features than other incoherent solitons.