Related papers: Exploring the ultimate limits: Super-resolution en…

In coherent diffractive imaging (CDI) the resolution of the reconstructed object is limited by the numerical aperture of the experimental setup. We present here a theoretical and numerical study for achieving super-resolution by…

This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…

Coherent enhancement is a powerful mechanism for improving the sensitivity of a wide range of detectors, but its practical use is often limited by the difficulty of preparing the required quantum states. We show that this difficulty has a…

Super-resolution estimation is the problem of recovering a stream of spikes (point sources) from the noisy observation of a few numbers of its first trigonometric moments. The performance of super-resolution is recognized to be intimately…

Quantum metrology of an incoherent signal is a canonical sensing problem related to superresolution and noise spectroscopy. We show that quantum computing can accelerate searches for a weak incoherent signal when the signal and noise are…

In its simplest form, decoherence occurs when a quantum state is entangled with a second state, but the results of measurements made on the second state are not accessible. As the second state has effectively "measured" the first, in this…

Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially…

Coherent ensembles of $N$ qubits present an advantage in quantum phase estimation over separable mixtures, but coherence decay due to classical phase diffusion reduces overall precision. In some contexts, the strength of diffusion may be…

The error in estimating the separation of a pair of incoherent sources from radiation emitted by them and subsequently captured by an imager is fundamentally bounded below by the inverse of the corresponding quantum Fisher information (QFI)…

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…

We consider the problem of determining the weights of a quantum ensemble. That is to say, given a quantum system that is in a set of possible known states according to an unknown probability law, we give strategies to estimate the…

We address the relation between quantum metrological resolution and coherence. We examine this dependence in two manners: we develop a quantum Wiener-Kintchine theorem for a suitable model of quantum ruler, and we compute the Fisher…

Coherent diffraction imaging is a high-resolution imaging technique whose potential can be greatly enhanced by applying the extrapolation method presented here. We demonstrate enhancement in resolution of a non-periodical object…

One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…

The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on…

Quantum coherence is the outcome of the superposition principle. Recently, it has been theorized as a quantum resource, and is the premise of quantum correlations in multipartite systems. It is therefore interesting to study the coherence…

A measurement is deemed successful, if one can maximize the information gain by the measurement apparatus. Here, we ask if quantum coherence of the system imposes a limitation on the information gain during quantum measurement. First, we…

Linear fusion of estimates under the condition of no knowledge of correlation of estimation errors has reached maturity. On the other hand, various cases of partial knowledge are still active research areas. A frequent motivation is to deal…

Quantum instruments derived from composite systems allow greater measurement precision than their classical counterparts due to coherences maintained between N components; spins, atoms or photons. Decoherence that plagues real-world devices…

Quantum measurements, alongside quantum states and processes, form a cornerstone of quantum information processing. However, unlike states and processes, their efficient characterisation remains relatively unexplored. We resolve this…