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We introduce quantum weighted entropy in analogy to an earlier notion of (classical) weighted entropy and derive many of its properties. These include the subadditivity, concavity and strong subadditivity property of quantum weighted…
We discuss the notions of mutual information and conditional information for noncomposite systems, classical and quantum; both the mutual information and the conditional information are associated with the presence of hidden correlations in…
A framework for categorizing entropic measures of nonclassical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum entropic quantity and the corresponding classical quantity…
We discuss conditional Renyi and Tsallis entropies for bipartite quantum systems of finite dimension. We investigate the relation between the positivity of conditional entropies and entanglement properties. It is in particular shown that…
Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…
We discuss the possibility of interpreting a q-deformed non-interacting system as incorporating the effects of interactions among its particles. This can be accomplished, for instance, in an ensemble of $q$-Bosons by means of the virial…
We discuss the notion of hidden correlations in classical and quantum indivisible systems along with such characteristics of the correlations as the mutual information and conditional information corresponding to the entropic subadditivity…
In this paper a general definition of quantum conditional entropy for infinite-dimensional systems is given based on recent work of Holevo and Shirokov arXiv:1004.2495 devoted to quantum mutual and coherent informations in the…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
The von Neumann entropy of various quantum dissipative models is calculated in order to discuss the entanglement properties of these systems. First, integrable quantum dissipative models are discussed, i.e., the quantum Brownian motion and…
Based on the form invariance of the structures given by Khinchin's axiomatic foundations of information theory and the pseudoadditivity of the Tsallis entropy indexed by q, the concept of conditional entropy is generalized to the case of…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to…
The two-parameter Minkowski like inequality written for composite quantum system state is obtained for arbitrary Hermitian nonnegative matrix with trace equal to unity. The inequality can be used as entropic and information inequality for…
We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…
We compare some recent computations of the entanglement of formation in quantum information theory and of the entropy of a subalgebra in quantum ergodic theory. Both notions require optimization over decompositions of quantum states. We…
Through the generalization of Khinchin's classical axiomatic foundation, a basis is developed for nonadditive information theory. The classical nonadditive conditional entropy indexed by the positive parameter q is introduced and then…
Quantum reference frames provide a relational description of multipartite quantum systems in which physical states and observables are defined relative to quantum observers. Yet different observers can assign different entropies to the same…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…