Related papers: Towards Nonadditive Quantum Information Theory

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about…

The information content of a source is defined in terms of the minimum number of bits needed to store the output of the source in a perfectly recoverable way. A similar definition can be given in the case of quantum sources, with qubits…

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…

For Tsallis' entropic analysis to the time evolutions of standard logistic map at the Feigenbaum critical point, it is known that there exists a unique value $q^*$ of the entropic index such that the asymptotic rate $K_q \equiv \lim_{t \to…

The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the…

Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…

The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak…

It is presented a generalization of the von Neumann mutual information in the context of Tsallis' nonextensive statistics. As an example, entanglement between two (two-level) quantum subsystems is discussed. Important changes occur in the…

The entropy shows an unavoidable tendency of disorder in thermostatistics according to the second thermodynamics law. This provides a minimization entropy principle for quantum thermostatistics with the von Neumann entropy and nonextensive…

We employ conditional Tsallis q entropies to study the separability of symmetric one parameter W and GHZ multiqubit mixed states. The strongest limitation on separability is realized in the limit q-->infinity, and is found to be much…

A quantum process encodes the causal structure that relates quantum operations performed in local laboratories. The process matrix formalism includes as special cases quantum mechanics on a fixed background space-time, but also allows for…

In this paper, new results on the analysis in hadron-hadron scattering are obtained by using the nonextensive quantum entropy and principle of minimum distance in the space of quantum states (PMD-SQS). Using Tsallis-like scattering…

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to…

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…

Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…

Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann- Gibbs form of the entropy ensures that…

We show that the conservation and the non-additivity of the information, together with the additivity of the entropy make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the…

In this manuscript we investigate quantum uncertainties in a Tsallis' non additive scenario. To such an end we appeal to q-exponentials, that are the cornerstone of Tsallis' theory. In this respect, it is found that some new mathematics is…

We discuss the discriminating power of separability criteria, which are based on the spectrum of a quantum state and its reductions. Common examples are entropic inequalities utilizing conditional Tsallis or Renyi entropies. We prove that…

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…