Related papers: Higher-order uncertainty bounds for mixed states
We consider the problem of approximating a general Gaussian location mixture by finite mixtures. The minimum order of finite mixtures that achieve a prescribed accuracy (measured by various $f$-divergences) is determined within constant…
We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3…
The Heisenberg uncertainty inequality is used to derive a rigorous lower bound to the amount of isospin impurities in $N=Z$ atomic nuclei, caused by the violation of isospin symmetry. The bound is fixed by the difference between the neutron…
In this paper we demonstrate the only available scalable information bounds for quantities of interest of high dimensional probabilistic models. Scalability of inequalities allows us to (a) obtain uncertainty quantification bounds for…
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
Given a pure state vector |x> and a density matrix rho, the function p(x|rho)=<x|rho|x> defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to…
Quantifying quantum mechanical uncertainty is vital for the increasing number of experiments that reach the uncertainty limited regime. We present a method for computing tight variance uncertainty relations, i.e., the optimal…
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 make two contributions to the problem of estimating the $L_1$ calibration error of a binary classifier from a finite dataset. First, we provide an upper bound for any classifier where the calibration function has bounded variation.…
The uncertainty relation for angle and angular momentum has a lower bound which depends on the form of the state. Surprisingly, this lower bound can be very large. We derive the states which have the lowest possible uncertainty product for…
A new lower boundary for the product of variances of two observables is obtained in the case, when these observables are entangled with the third one. This boundary can be higher than the Robertson--Schr\"odinger one. The special case of…
We consider the effect of parametric uncertainty on properties of Linear Time Invariant systems. Traditional approaches to this problem determine the worst-case gains of the system over the uncertainty set. Whilst such approaches are…
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by…
Prompted by the open questions in Gibilisco [Int. J. Software Informatics, 8(3-4): 265, 2014], in which he introduced a family of measurement-induced quantum uncertainty measures via metric adjusted skew informations, we investigate these…
The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
When an optimal measurement is made on a qubit and what we call an Unbiased Mixture of the resulting ensembles is taken, then the post measurement density matrix is shown to be related to the pre-measurement density matrix through a simple…
In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only…
We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…