Related papers: Tight entropic uncertainty relations for systems w…
We analyze the uncertainty relation for the sum of variances, which is called in some papers, the stronger uncertainty relation for all incompatible observables. We show that this uncertainty relation for the sum of variances of the…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…
Sharp uncertainty relations restricting the values of variances in the position space and in the momentum (wavevector) space are derived. They have the same form $\Delta r\Delta k\ge 5/2$ in the classical theory of light beams, in the…
We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…
Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the…
The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In the literature, many experiments have been devoted to the test of the…
Uncertainty relations are pivotal in delineating the limits of simultaneous measurements for observables. In this paper, we derive four novel uncertainty and reverse uncertainty relations for the sum of variances of two incompatible…
Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator…
It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
We conjecture a new entropic uncertainty principle governing the entropy of complementary observations made on a system given side information in the form of quantum states, generalizing the entropic uncertainty relation of Maassen and…
We define the entropy S and uncertainty function of a squeezed system interacting with a thermal bath, and study how they change in time by following the evolution of the reduced density matrix in the influence functional formalism. As…
The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find…
Recently, an entropic uncertainty relation for multiple measurements has been proposed by Liu et al. in [Phys. Rev. A 91, 042133 (2015)]. However, the lower bound of the relation is not always tight with respect to different measurements.…
We derive a fine-grained uncertainty relation for the measurement of two incompatible observables on a single quantum system of continuous variables, and show that continuous variable systems are more uncertain than discrete variable…
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…
The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…