Related papers: Asymptotic entropic uncertainty relations
A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are…
We study a possible improvement of uncertainty relations. The Heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables. The Schroedinger uncertainty…
There is a renewed interest in the uncertainty principle, reformulated from the information theoretic point of view, called the entropic uncertainty relations. They have been studied for various integrable systems as a function of their…
This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
Universally valid uncertainty relations are proven in a model independent formulation for inherent and unavoidable extra noises in arbitrary joint measurements on single systems, from which Heisenber's original uncertainty relation is…
We introduce a new measure of interdependence among the components of a random vector along the main diagonal of the vector copula, i.e. along the line $u_{1}=\ldots=u_{J}$, for $\left(u_{1},\ldots,u_{J}\right)\in\left[0,1\right]^{J}$. Our…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is…
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…
We study the time evolution of the reduced Wigner function for a class of quantum Brownian motion models. We derive two generalized uncertainty relations. The first consists of a sharp lower bound on the uncertainty function, $U = (\Delta…
We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy-Schwarz…
We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental…
We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…
Uncertainties in successive measurements of general canonically conjugate variables are examined. Such operators are approached within a limiting procedure of the Pegg-Barnett type. Dealing with unbounded observables, we should take into…
We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…
In this paper we derive a new quantum entropic uncertainty relation, bounding the conditional smooth quantum min entropy based on the result of a measurement using a two outcome POVM and the failure probability of a classical sampling…
We generalize, improve and unify theorems of Rumin, and Maassen--Uffink about classical entropies associated to quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different…