Related papers: New Perspectives and some Celebrated Quantum Inequ…
Quantum entropy inequalities are studied. Some quantum entropy inequalities are obtained by several methods. For entanglement breaking channel, we show that the entanglement-assisted classical capacity is upper bounded by $\log d$. A…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex…
We derive new characterisations of the matrix $\mathrm{\Phi}$-entropy functionals introduced in [Electron.~J.~Probab., 19(20): 1--30, 2014]. Notably, all known equivalent characterisations of the classical $\Phi$-entropies have their matrix…
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one,…
Relativistic effects affect nearly all notions of quantum information theory. The vacuum behaves as a noisy channel, even if the detectors are perfect. The standard definition of a reduced density matrix fails for photon polarization…
After an elementary derivation of Bell's inequality, several forms of expectation functions for two-valued observables are discussed. Special emphasis is given to hypothetical stronger-than quantum expectation functions which give rise to a…
The joint convexity of the map $(X,A) \mapsto X^* A^{-1} X$, an integral representation of operator convex functions, and an observation of Ando are used to obtain a simple proof of both the joint convexity of relative entropy and a trace…
In this work the Quantum and Statistical Mechanics of the Early Universe, i.e. at Planck scale, is considered as a deformation of the well-known theories. In so doing the primary object under deformation in both cases is the density matrix.…
We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity…
The novel concept of quantum logical entropy is presented and analyzed. We prove several basic properties of this entropy with regard to density matrices. We hereby motivate a different approach for the assignment of quantum entropy to…
We introduce a new interpretation of quantum mechanics by examining the Einstein, Podolsky and Rosen's (EPR) paradox and Bell's inequality experiments under the assumption that the vacuum has an inhomogeneous texture for energy levels below…
Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use…
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…
We show that the "practical" Bell inequalities, which use intensities as the observed variables, commonly used in quantum optics and widely accepted in the community, suffer from an inherent loophole, which severely limits the range of…
We review the fundamental properties of the quantum relative entropy for finite-dimensional Hilbert spaces. In particular, we focus on several inequalities that are related to the second law of thermodynamics, where the positivity and the…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
In this article, we prove that convex functions and log-convex functions obey certain general refinements that lead to several refinements and reverses of well known inequalities for matrices, including Young's inequality, Heinz inequality,…