Related papers: New Perspectives and some Celebrated Quantum Inequ…
This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special…
The logical foundations of Bell's inequality are reexamined. We argue that the form of the reality condition that underpins Bell's inequality comes from the requirement of solving the quantum measurement problem. Hence any violation of…
We give some new refinements of Heinz inequality and an improvement of the reverse Young's inequality for scalars and we use them to establish new inequalities for operators and the Hilbert-Schmidt norm of matrices. We give a uniformly and…
In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is…
We analyze the Schwarz inequality and its generalizations, as well as inequalities resulting from the Jensen inequality. They are used in quantum theory to derive the Heisenberg-Robertson (HR) and Schroedinger-Robertson (SR) uncertainty…
The summary of the Author's results on Bell inequalities and macroscopic entanglement.
We derive entropic Bell inequalities from considering entropy Venn diagrams. These entropic inequalities, akin to the Braunstein-Caves inequalities, are violated for a quantum mechanical Einstein-Podolsky-Rosen pair, which implies that the…
Quantum coherence and entanglement are two key features in quantum mechanics and play important roles in quantum information processing and quantum computation. We provide a general triangle-like inequality satisfied by the $l_1$-norm…
In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that…
Many important properties of quantum channels are quantified by means of entropic functionals. Characteristics of such a kind are closely related to different representations of a quantum channel. In the Jamio{\l}kowski-Choi representation,…
Various quantum thermodynamic bounds are shown to stem from a single tighter and more general inequality, consequence of the operator concavity of the logarithmic function. Such an inequality, which we call the "thermodynamic reverse…
Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These…
We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
An operator equality on the entropy production for general quantum Markovian master equations is derived without resorting quantum stochastic trajectory and priori quantum definition of entropy production. We find that, the equality can be…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
Mercer inequality for convex functions is a variant of Jensen's inequality, with an operator version that is still valid without operator convexity. This paper is two folded. First, we present a Mercer-type inequality for operators without…
We develop a new framework for the Jensen-type inequalities that allows us to deal with functions not necessarily convex and Borel measures not necessarily positive.
We provide a framework for Bell inequalities which is based on multilinear contractions. The derivation of the inequalities allows for an intuitive geometric depiction and their violation within quantum mechanics can be seen as a direct…
We show that the thermal subadditivity of entropy provides a common basis to derive a strong form of the bounded difference inequality and related results as well as more recent inequalities applicable to convex Lipschitz functions, random…