Information Theory based on Non-additive Information Content

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 entropy. Some general properties of the nonadditive information entropy are studied, in addition, the relation between the nonadditivity $q$ and the codeword length is pointed out.Comment: 9 pages, no figures, RevTex, accepted for publication in Phys. Rev. E(an error in proof of theorem 1 was corrected, typos corrected

Long range intermolecular forces in triatomic systems: connecting the atom-diatom and atom-atom-atom representations

The long-range forces that act between three atoms are analysed in both atom-diatom and atom-atom-atom representations. Expressions for atom-diatom dispersion coefficients are obtained in terms of 3-body nonadditive coefficients. The anisotropy of atom-diatom C_6 dispersion coefficients arises primarily from nonadditive triple-dipole and quadruple-dipole forces, while pairwise-additive forces and nonadditive triple-dipole and dipole-dipole-quadrupole forces contribute significantly to atom-diatom C_8 coefficients. The resulting expressions are applied to dispersion coefficients for Li + Li_2 (triplet) and recommendations are made for the best way to obtain global triatomic potentials that dissociate correctly both to three separated atoms and to an atom and a diatomic molecule.Comment: To be published in a special issue of Molecular Physics in honour of Mark Chil

Thermodynamic stability conditions for nonadditive composable entropies

The thermodynamic stability conditions (TSC) of nonadditive and composable entropies are discussed. Generally the concavity of a nonadditive entropy with respect to internal energy is not necessarily equivalent to the corresponding TSC. It is shown that both the TSC of Tsallis' entropy and that of the $\kappa$-generalized Boltzmann entropy are equivalent to the positivity of the standard heat capacity.Comment: 6pages; Contribution to a topical issue of Continuum Mechanics and Thermodynamics (CMT), edited by M. Sugiyam

Nonadditive conditional entropy and its significance for local realism

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 nonadditive (nonextensive) composite systems. The proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum context, indicating its utility for characterizing quantum entanglement. A criterion deduced from it for separability of density matrices for validity of local realism is examined in detail by employing a bipartite spin-1/2 system. It is found that the strongest criterion is obtained in the limit q going to infinity.Comment: 12 pages, 1 figur

Graphical Nonbinary Quantum Error-Correcting Codes

In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which results in many interesting codes including some nonadditive codes meeting the Singleton bounds, we are able to construct explicitly four families of optimal codes, namely, $[[6,2,3]]_p$, $[[7,3,3]]_p$, $[[8,2,4]]_p$ and $[[8,4,3]]_p$ for any odd dimension $p$ and a family of nonadditive code $((5,p,3))_p$ for arbitrary $p>3$. In the case of composite numbers as dimensions, we also construct a family of stabilizer codes $((6,2\cdot p^2,3))_{2p}$ for odd $p$, whose coding subspace is {\em not} of a dimension that is a power of the dimension of the physical subsystem.Comment: 12 pages, 5 figures (pdf

Non-Pauli Observables for CWS Codes

It is known that nonadditive quantum codes are more optimal for error correction when compared to stabilizer codes. The class of codeword stabilized codes (CWS) provides tools to obtain new nonadditive quantum codes by reducing the problem to finding nonlinear classical codes. In this work, we establish some results on the kind of non-Pauli operators that can be used as decoding observables for CWS codes and describe a procedure to obtain these observables

Multicomponent fluid of nonadditive hard spheres near a wall

A recently proposed rational-function approximation [Phys. Rev. E \textbf{84}, 041201 (2011)] for the structural properties of nonadditive hard spheres is applied to evaluate analytically (in Laplace space) the local density profiles of multicomponent nonadditive hard-sphere mixtures near a planar nonadditive hard wall. The theory is assessed by comparison with $NVT$ Monte Carlo simulations of binary mixtures with a size ratio 1:3 in three possible scenarios: a mixture with either positive or negative nonadditivity near an additive wall, an additive mixture with a nonadditive wall, and a nonadditive mixture with a nonadditive wall. It is observed that, while the theory tends to underestimate the local densities at contact (especially in the case of the big spheres) it captures very well the initial decay of the densities with increasing separation from the wall and the subsequent oscillations.Comment: 10 pages, 7 figures; v2: improved version plus a new figur