Related papers: Uncertainty principles for the imaginary Ornstein-…
In this paper, we systematically investigate the Heisenberg-Pauli-Weyl uncertainty principle for free metaplectic transformation, as well as metaplectic operators. Specifically, we obtain two different types of the uncertainty principle for…
Recently, universally valid uncertainty relations have been established to set a precision limit for any instruments given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to…
A solution is given to a conjecture proposed by Y. Wigderson and A. Wigderson concerning a "Heisenberg-like" uncertainty principle. This is an old article already published in 2022.
Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a quantum system. However, if the observer has access to a…
In this paper we prove stable determination of an inverse boundary value problem associated to a magnetic Schr\"odinger operator assuming that the magnetic and electric potentials are essentially bounded and the magnetic potentials admit a…
In this article we study the Schr\"odinger equation associated with Harmonic oscillator in the form of Strichartz type inequality. We give simple proofs for Strichartz type inequalities using purely the $L^2 \to L^p$ operator norm estimates…
We derive the lower bound of uncertainty relations of two unitary operators for a class of states based on the geometric-arithmetic inequality and Cauchy-Schwarz inequality. Furthermore, we propose a set of uncertainty relations for three…
If $Q$ is a real, symmetric and positive definite $n\times n$ matrix, and $B$ a real $n\times n$ matrix whose eigenvalues have negative real parts, we consider the Ornstein--Uhlenbeck semigroup on $\mathbb{R}^n$ with covariance $Q$ and…
The aim of this paper is to prove an uncertainty principle for the representation of a vector in two bases. Our result extends previously known qualitative uncertainty principles into quantitative estimates. We then show how to transfer…
As a time-shifted and frequency-modulated version of the linear canonical transform (LCT), the offset linear canonical transform (OLCT) provides a more general framework of most existing linear integral transforms in signal processing and…
We study the stability of the Schr\"odinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schr\"odinger equation by the difference of their…
Quantum theory is notoriously counterintuitive, and yet remains entirely self-consistent when applied universally. Here we uncover a new manifestation of its unusual consequences. We demonstrate, theoretically and experimentally (by means…
In this note we present a notion of harmonic oscillator on the Heisenberg group $\mathbf{H}_n$ which forms the natural analogue of the harmonic oscillator on $\mathbb{R}^n$ under a few reasonable assumptions: the harmonic oscillator on…
We reformulate the notion of uncertainty of pairs of unitary operators within the context of guessing games and derive an entropic uncertainty relation for a pair of such operators. We show how distinguishable operators are compatible while…
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…
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…
We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our…
Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report improved new versions of various error-disturbance tradeoff relations…
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…
We continue our previous study of improved Hardy, Rellich and Uncertainty principle inequalities on a Riemannian manifold $M$, started in \cite{Kombe-Ozaydin}. In the present paper we prove new weighted Hardy-Poincar\'e, Rellich type…