Related papers: Bounds on general entropy measures
We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts…
Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
One of the most counterintuitive aspects of quantum theory is its claim that there is 'intrinsic' randomness in the physical world. Quantum information science has greatly progressed in the study of intrinsic, or secret, quantum randomness…
We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…
What can we learn about entanglement between individual particles in macroscopic samples by observing only the collective properties of the ensembles? Using only a few experimentally feasible collective properties, we establish an…
A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally…
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…
We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum…
The most fundamental properties of quantum entropy are derived by considering the union of two ensembles. We discuss the limits these properties put on an entropy measure and obtain that they uniquely determine the form of the entropy…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an…
We present two new estimators for estimating the entropy of absolutely continuous random variables. Some properties of them are considered, specifically consistency of the first is proved. The introduced estimators are compared with the…
We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…