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Spatial-mode projective measurements could achieve super-resolution in remote sensing and imaging, yet their performance is usually sensitive to the parameters of the target scenes. We propose and demonstrate a robust classifier of close-by light sources by using optimized mode projection via nonlinear optics. Contrary to linear-optics based methods using the first few Hermite-Gaussian modes for the projection, here the projection modes are optimally tailored by shaping the pump wave to drive the nonlinear optical process. This minimizes modulation losses and allows high flexibility in designing those modes for robust and efficient measurements. We test this classifier on discriminating one light source and two sources separated well within the Rayleigh limit without prior knowledge of the exact centroid or brightness. Our results show a classification fidelity of over 80% even when the centroid is misaligned by half the source separation, or when one source is four times stronger than the other.

We demonstrate a chip-integrated emission spectroscope capable of retrieving the temperature of the light sources. It consists of a single photon detector with low dark counts and a sweeping on-chip filter with 2 pm spectral resolution in the visible and near-infrared regimes. With wildfire sensing applications in mind, we test our system with a hollow cathode lamp to simulate the K-line emission, and show how the models of Doppler and collision broadening in the plasma can be used for temperature retrieval. With favorable device parameters, high spectral resolution, and a novel temperature retrieval capability, our technique may find broad applications in environmental monitoring, astrophysics, plasma physics, and so on., Comment: 12 pages, 13 figures

Quantum techniques are expected to revolutionize how information is acquired, exchanged, and processed. Yet it has been a challenge to realize and measure their values in practical settings. We present first photon machine learning as a new paradigm of neural networks and establish the first unambiguous advantage of quantum effects for artificial intelligence. By extending the physics behind the double-slit experiment for quantum particles to a many-slit version, our experiment finds that a single photon can perform image recognition at around $30\%$ fidelity, which beats by a large margin the theoretical limit of what a similar classical system can possibly achieve (about 24\%). In this experiment, the entire neural network is implemented in sub-attojoule optics and the equivalent per-calculation energy cost is below $10^{-24}$ joule, highlighting the prospects of quantum optical machine learning for unparalleled advantages in speed, capacity, and energy efficiency., Comment: 19 pages, 5 figures

The Hellinger distance between quantum states is a significant measure in quantum information theory, known for its Riemannian and monotonic properties. It is also easier to compute than the Bures distance, another measure that shares these properties. In this work, we derive the mean and variance of the Hellinger distance between pairs of density matrices, where one or both matrices are random. Along the way, we also obtain exact results for the mean affinity and mean square affinity. The first two cumulants of the Hellinger distance allow us to propose an approximation for the corresponding probability density function based on the gamma distribution. Our analytical results are corroborated through Monte Carlo simulations, showing excellent agreement., Comment: 8 pages, 5 figures

Discerning chaos in quantum systems is an important problem as the usual route of Lyapunov exponents in classical systems is not straightforward in quantum systems. A standard route is the comparison of statistics derived from model physical systems to those from random matrix theory (RMT) ensembles, of which the most popular is the nearest-neighbour-spacings distribution (NNSD), which almost always shows good agreement with chaotic quantum systems. However, even in these cases, the long-range statistics (like number variance, spectral rigidity etc.), which are also more difficult to calculate, often show disagreements with RMT. As such, a more stringent test for chaos in quantum systems, via an analysis of intermediate-range statistics is needed, which will additionally assess the extent of agreement with RMT universality. In this paper, we deduce the effective level-repulsion parameters and the corresponding Wigner-surmise-like results of the next-nearest-neighbor spacing distribution (nNNSD) for integrable systems (semi-Poissonian statistics) as well as the three classical quantum-chaotic Wigner-Dyson regimes, by stringent comparisons to numerical RMT models and benchmarking against our exact analytical results for $3\times 3$ Gaussian matrix models, along with a semi-analytical form for the nNNSD in the Orthogonal-to-Unitary symmetry crossover. To illustrate the robustness of these RMT based results, we test these predictions against the nNNSD obtained from quantum chaotic models as well as disordered lattice spin models. This reinforces the Bohigas-Giannoni-Schmit and the Berry-Tabor conjectures, extending the associated universality to longer range statistics. In passing, we also highlight the equivalence of nNNSD in the apparently distinct Orthogonal-to-Unitary and diluted-Symplectic-to-Unitary crossovers., Comment: 19 Pages, 15 Figures

The dissipative spectral form factor (DSFF) has recently emerged as a diagnostic tool for assessing non-integrability or chaos in non-Hermitian systems. It extends the concept of the spectral form factor (SFF), a widely used measure for similar investigations in Hermitian systems. In this study, we concentrate on the elliptic Ginibre unitary ensemble (eGinUE), which interpolates between the non-Hermitian limit of Ginibre unitary ensemble (GinUE) and the Hermitian limit of Gaussian unitary ensemble (GUE) by varying a symmetry parameter. We derive exact finite-dimension expression and large-dimension approximation for the DSFF of eGinUE. A key finding of this work is a compelling ``scaling relationship" between the DSFF of eGinUE and that of the GUE or GinUE. This scaling relationship also reveals a previously unobserved connection between the DSFF of GinUE and the SFF of GUE. The DSFF for eGinUE displays a \emph{dip-ramp-plateau} structure in the GinUE and GUE limits, as well as in the crossover region, with differences in time scales that are well-explained by the aforementioned scaling relationship. Additionally, depending on the symmetry regime within the crossover, we provide various estimates for the Thouless time ($T_\mathrm{Th}$) and Heisenberg time ($T_\mathrm{H}$), which correspond to the dip-ramp and ramp-plateau transitions, respectively. Our analytical results are compared with Monte Carlo simulations of the eGinUE random matrix model, showing excellent agreement., Comment: 9 pages, 3 figures

Wearable sensors enable health researchers to continuously collect data pertaining to the physiological state of individuals in real-world settings. However, such data can be subject to extensive missingness due to a complex combination of factors. In this work, we study the problem of imputation of missing step count data, one of the most ubiquitous forms of wearable sensor data. We construct a novel and large scale data set consisting of a training set with over 3 million hourly step count observations and a test set with over 2.5 million hourly step count observations. We propose a domain knowledge-informed sparse self-attention model for this task that captures the temporal multi-scale nature of step-count data. We assess the performance of the model relative to baselines and conduct ablation studies to verify our specific model designs., Comment: Accepted by Conference on Health, Inference, and Learning (CHIL) 2024