Related papers: Sequences with Minimal Time-Frequency Uncertainty
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's Uncertainty Principle," Heisenberg originally formulated his ideas in terms of a relationship between…
A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained, and extended from N-dimensional Fourier transform domain to two N-dimensional…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
Time-frequency concentration and resolution of the Cohen's class time-frequency distribution (CCTFD) has attracted much attention in time-frequency analysis. A variety of uncertainty principles of the CCTFD is therefore derived, including…
Signal processing on graphs is a recent research domain that aims at generalizing classical tools in signal processing, in order to analyze signals evolving on complex domains. Such domains are represented by graphs, for which one can…
In this work, we consider the problem of bounding the values of a covariance function corresponding to a continuous-time stationary stochastic process or signal. Specifically, for two signals whose covariance functions agree on a finite…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
We provide evidence that the uncertainty in detection of small and deterministic phase-shift deviations from a working point can be lower than the Heisenberg bound, for fixed finite mean number of photons. We achieve that by exploiting…
One of the most widely known building blocks of modern physics is Heisenberg's indeterminacy principle. Among the different statements of this fundamental property of the full quantum mechanical nature of physical reality, the uncertainty…
Uncertainty principles present an important theoretical tool in signal processing, as they provide limits on the time-frequency concentration of a signal. In many real-world applications the signal domain has a complicated irregular…
The Heisenberg time-energy relation prevents determination of an atomic transition to better than the inverse of the measurement time. The relation generally applies to frequency estimation of a near-resonant field [1-3], since information…
The core of Heisenberg's heuristic argument for the uncertainty principle, involving the famous $\gamma$-ray microscope $\textit{Gedankenexperiment}$, hinges upon the existence of measurements that irreversibly alter the state of the system…
The Heisenberg limit is acknowledged as the ultimate precision limit in quantum metrology, traditionally implying that root mean square errors of parameter estimation decrease linearly with the time T of evolution and the number N of…
A central feature of quantum metrology is the possibility of Heisenberg scaling, a quadratic improvement over the limits of classical statistics. This scaling, however, is notoriously fragile to noise. While for some noise types it can be…
Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process…
Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the…
The classical uncertainty principle of harmonic analysis states that a nontrivial function and its Fourier transform cannot both be sharply localized. It plays an important role in signal processing and physics. This paper generalizes the…
The past several years have witnessed a surge of research investigating various aspects of sparse representations and compressed sensing. Most of this work has focused on the finite-dimensional setting in which the goal is to decompose a…