Related papers: Uncertainty principle, Shannon-Nyquist sampling an…
We study the problem of sampling a random signal with sparse support in frequency domain. Shannon famously considered a scheme that instantaneously samples the signal at equispaced times. He proved that the signal can be reconstructed as…
We study trade-off relations in information extraction from quantum systems subject to null-result weak measurements, where the absence of a detected photon continuously updates the system state. We present a detailed analysis of qubit and…
We show that quantum-to-classical channels, i.e., quantum measurements, can be asymptotically simulated by an amount of classical communication equal to the quantum mutual information of the measurement, if sufficient shared randomness is…
As a very fundamental principle in quantum physics, uncertainty principle has been studied intensively via various uncertainty inequalities. Based on the information measure introduced by Brukner and Zeilinger in [Phys. Rev. Lett. 83, 3354…
Uncertainty sampling is a prevalent active learning algorithm that queries sequentially the annotations of data samples which the current prediction model is uncertain about. However, the usage of uncertainty sampling has been largely…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…
We derive a tight bound between the quality of estimating a quantum state by measurement and the success probability of undoing the measurement in arbitrary dimensional systems, which completely describes the tradeoff relation between the…
We present some forms of uncertainty principle which involve in a new way localization operators, the concept of $\varepsilon$-concentration and the standard deviation of $L^2$ functions. We show how our results improve the classical…
This paper presents a tutorial for CS applications in communications networks. The Shannon's sampling theorem states that to recover a signal, the sampling rate must be as least the Nyquist rate. Compressed sensing (CS) is based on the…
All measurements of continuous signals rely on taking discrete snapshots, with the Nyquist-Shannon theorem dictating sampling paradigms. We present a broader framework of information-optimal measurement, showing that traditional sampling is…
Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…
This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle can be derived by the postulate of finite transmission speed of light and information . The theory shows…
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…
Signal sampling and reconstruction is a fundamental engineering task at the heart of signal processing. The celebrated Shannon-Nyquist theorem guarantees perfect signal reconstruction from uniform samples, obtained at a rate twice the…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
Signal processing and Information theory are two disparate fields used for characterizing signals for various scientific and engineering applications. Spectral/Fourier analysis, a technique employed in signal processing, helps estimation of…
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…
We derive fundamental sampling bounds for smooth signals in continuous settings without sparsity assumptions. By introducing the Fourier ratio as a measure of spectral compressibility induced by smoothness, we obtain explicit, deterministic…