Related papers: Information theory with finite vector spaces
The single qudit state tomograms are shown to have the no signaling property. The known and new entropic and information inequalities for Shannon, von Neumann and q-entropies of the composite and noncomposite systems characterizing…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized…
In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual…
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
We generalize the Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive…
Information entropies give a genuine way to characterize quantitatively an incompatibility in quantum measurements. Together with the Shannon entropy, few families of parametrized entropies have found use in various questions. It is also…
We study the properties of Tsallis entropy and Shannon entropy from the point of view of algorithmic randomness. In algorithmic information theory, there are two equivalent ways to define the program-size complexity K(s) of a given finite…
In this paper we extend our recent results [Physica A340 (2004)110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Renyi with the q-deformed version of Khinchin axioms to obtain the…
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…
We have discussed the Tsallis entropy in finite $N$-unit nonextensive systems, by using the multivariate $q$-Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the…
Two-dimensional Yang-Mills theory is a useful model of an exactly solvable gauge theory with a string theory dual at large $N$. We calculate entanglement entropy in the $1/N$ expansion by mapping the theory to a system of $N$ fermions…
We consider statistically independent non-identical subsystems with different entropic indices q1 and q2. A relation between q1, q2 and q' (for the entire system) extends a power law for entropic index as a function of distance r. A few…
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…
We give a new proof of the theorems on the maximum entropy principle in Tsallis statistics. That is, we show that the $q$-canonical distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the…
There is an asymptotic relationship between the multiplicative relations among multinomial coefficients and the (additive) recurrence property of Shannon entropy known as the chain rule. We show that both types of identities are…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…