Related papers: Optimized entropic uncertainty relations for multi…
We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…
We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that…
We study uncertainty and certainty relations for two successive measurements of two-dimensional observables. Uncertainties in successive measurement are considered within the following two scenarios. In the first scenario, the second…
We present observable upper bounds of squared concurrence, which are the dual inequalities of the observable lower bounds introduced in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98, 140505 (2007)] and [L. Aolita, A. Buchleitner and…
Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be…
The resource theoretic measure of quantum coherence is basis dependent, and the amount of coherence contained in a state is different in different bases. We obtained analytical solutions for the maximum coherence by optimizing the reference…
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…
We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ),…
Reality of quantum observables, a feature of long-standing interest within foundations of quantum mechanics, has recently been quantified and deeply studied by means of entropic measures [Phys. Rev. A 97, 022107 (2018)]. However, there is…
Uncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, was…
We derive an optimal entropic uncertainty relation for an arbitrary pair of observables in a two-dimensional Hilbert space. Such a result, for the simple case we are considering, definitively improves all the entropic uncertainty relations…
We investigate the uncertainty associated with a joint quantum measurement of two components of spin of a spin-1/2 particle and quantify this in terms of entropy. We consider two entropic quantities: the joint entropy and the sum of the…
One of the defining traits of quantum mechanics is the uncertainty principle which was originally expressed in terms of the standard deviation of two observables. Alternatively, it can be formulated using entropic measures, and can also be…
Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state…
We consider two entropic uncertainty relations of position and momentum recently discussed in literature. By a suitable rescaling of one of them, we obtain a smooth interpolation of both for high-resolution and low-resolution measurements…
The Holevo bound is a bound on the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound which reduces to the…
Information entropies provide powerful and flexible way to express restrictions imposed by the uncertainty principle. This approach seems to be very suitable in application to problems of quantum information theory. It is typical that…
Heisenberg's uncertainty relations for measurement quantify how well we can jointly measure two complementary observables and have attracted much experimental and theoretical attention recently. Here we provide an exact tradeoff between the…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs…