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We develop a robust uncertainty principle for finite signals in C^N which states that for almost all subsets T,W of {0,...,N-1} such that |T|+|W| ~ (log N)^(-1/2) N, there is no sigal f supported on T whose discrete Fourier transform is…

Linear optical elements are pivotal instruments in the manipulation of classical and quantum states of light. The vast progress in integrated quantum photonic technology enables the implementation of large numbers of such elements on chip…

In a recent article [1] we have explored alternative decompositions of the Lorentz transformation by adopting the synchronization convention of the target frame at the end and alternately at the outset. In this note we develop the…

Conventional Fourier-domain Optical Coherence Tomography (FD-OCT) systems depend on resampling into wavenumber (k) domain to extract the depth profile. This either necessitates additional hardware resources or amplifies the existing…

The inductive bias of a neural network is largely determined by the architecture and the training algorithm. To achieve good generalization, how to effectively train a neural network is of great importance. We propose a novel orthogonal…

In this paper, we establish analogs of Miyachi, Cowling-Price, and Heisenberg-Pauli-Weyl uncertainty principles in the framework of the linear canonical Dunkl transform. We also obtain some weighted inequalities, such as Nash, Clarkson,…

Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…

Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…

Certification is important to guarantee the correct functioning of quantum devices. A key certification task is verifying that a device has produced a desired output state. In this work, we study this task in the context of photonic…

Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A…

In the context of optical signal processing, quantum and quantum-inspired machine learning algorithms have massive potential for deployment. One of the applications is in error correction protocols for the received noisy signals. In some…

Computational corrections of defocus and aberrations in optical coherence tomography (OCT) offers a promising approach to realize high-resolution imaging with deep imaging depth, but without additional high hardware costs. However, these…

Optical coherence tomography (OCT) is a widely used imaging technique in the micrometer regime, which gained accelerating interest in medical imaging in the last twenty years. In up-to-date OCT literature [5,6] certain simplifying…

Autonomous vehicles that navigate in open-world environments may encounter previously unseen object classes. However, most existing LiDAR panoptic segmentation models rely on closed-set assumptions, failing to detect unknown object…

Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…

Diffractive optical information processors have demonstrated significant promise in delivering high-speed, parallel, and energy efficient inference for scaling machine learning tasks. Training, however, remains a major computational…

Deep neural networks have achieved remarkable success across a variety of tasks, yet they often suffer from unreliable probability estimates. As a result, they can be overconfident in their predictions. Conformal Prediction (CP) offers a…

Optical link tomography (OLT) is a rapidly evolving field that allows the multi-span, end-to-end visualization of optical power along fiber links in multiple dimensions from network endpoints, solely by processing signals received at…

In this paper we present a framework for the design and implementation of offset equivariant networks, that is, neural networks that preserve in their output uniform increments in the input. In a suitable color space this kind of networks…

Neural networks are often utilised in critical domain applications (e.g. self-driving cars, financial markets, and aerospace engineering), even though they exhibit overconfident predictions for ambiguous inputs. This deficiency demonstrates…