Related papers: Generalised Pinching Inequality
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
The direct part of Stein's lemma in quantum hypothesis testing is revisited based on a key operator inequality between a density operator and its pinching. The operator inequality is used to show a simple proof of the direct part of Stein's…
Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…
In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…
We show a general relationship between a superposition of macroscopically distinct states and sensitivity in quantum metrology. Generalized cat states are defined by using an index which extracts the coherence between macroscopically…
We propose the gentle measurement principle (GMP) as one of the principles at the foundation of quantum mechanics. It asserts that if a set of states can be distinguished with high probability, they can be distinguished by a measurement…
We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass. This generalization inherits the convexity and computational efficiency from the…
Measurement is of central interest in quantum mechanics as it provides the link between the quantum world and the world of everyday experience. One of the features of the latter is its robust, objective character, contrasting the delicate…
The rapid developments of Quantum Information Science (QIS) have opened up new avenues for exploring fundamental physics. Quantum nonlocality, a key aspect for distinguishing quantum information from classical one, has undergone extensive…
This article proposes a novel algorithm for solving mismatch problem in compressed sensing. Its core is to transform mismatch problem into matched by constructing a new measurement matrix to match measurement value under unknown measurement…
We are concerned with log-majorization for matrices in connection with the multivariate Golden--Thompson trace inequality and the Karcher mean (i.e., a multivariate extension of the weighted geometric mean). We show an extension of Araki's…
Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metric $\bar{d}_1$ that combines…
This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM). The generalized concentrability condition establishes a framework that interpolates…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
We develop a unified strategy to obtain the geometric logarithmic Hardy inequality on any open set M of a stratified group, provided the validity of the Hardy inequality in this setting, where the so-called "weight" is regarded to be any…
Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…