Improving Detectors Using Entangling Quantum Copiers

We present a detection scheme which using imperfect detectors, and imperfect quantum copying machines (which entangle the copies), allows one to extract more information from an incoming signal, than with the imperfect detectors alone.Comment: 4 pages, 2 figures, REVTeX, to be published in Phys. Rev.

Quantum information entropies of the eigenstates and the coherent state of the P\"oschl-Teller potential

The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for the first excited state, for different strengths of the potential well, are then numerically obtained. Interesting features of the entropy densities, owing their origin to the excited nature of the wave functions, are graphically demonstrated. We then compute the position space entropies of the coherent state of the P\"oschl-Teller potential, which is known to show revival and fractional revival. Time evolution of the coherent state reveals many interesting patterns in the space-time flow of information entropy.Comment: Revtex4, 11 pages, 11 eps figures and a tabl

Detecting the harmonics of oscillations with time-variable frequencies

A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology

Group entropies, correlation laws and zeta functions

The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are presented, related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium, when the dynamics is weakly chaotic. The associated thermostatistics are discussed. The mathematical structure underlying our construction is that of formal group theory, which provides the general structure of the correlations among particles and dictates the associated entropic functionals. As an example of application, the role of group entropies in information theory is illustrated and generalizations of the Kullback-Leibler divergence are proposed. A new connection between statistical mechanics and zeta functions is established. In particular, Tsallis entropy is related to the classical Riemann zeta function.Comment: to appear in Physical Review

Exploring the randomness of Directed Acyclic Networks

The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs (DAGs). An important ingredient of the analysis of such networks is a proper comparison of their observed architecture against an ensemble of randomized graphs, thereby quantifying the {\em randomness} of the real systems with respect to suitable null models. This approximation is particularly relevant when the finite size and/or large connectivity of real systems make inadequate a comparison with the predictions obtained from the so-called {\em configuration model}. In this paper we analyze four methods of DAG randomization as defined by the desired combination of topological invariants (directed and undirected degree sequence and component distributions) aimed to be preserved. A highly ordered DAG, called \textit{snake}-graph and a Erd\:os-R\'enyi DAG were used to validate the performance of the algorithms. Finally, three real case studies, namely, the \textit{C. elegans} cell lineage network, a PhD student-advisor network and the Milgram's citation network were analyzed using each randomization method. Results show how the interpretation of degree-degree relations in DAGs respect to their randomized ensembles depend on the topological invariants imposed. In general, real DAGs provide disordered values, lower than the expected by chance when the directedness of the links is not preserved in the randomization process. Conversely, if the direction of the links is conserved throughout the randomization process, disorder indicators are close to the obtained from the null-model ensemble, although some deviations are observed.Comment: 13 pages, 5 figures and 5 table

Information transfer and fidelity in quantum copiers

We find that very different quantum copying machines are optimal depending on the indicator used to assess their performance. Several quantum copying machine models acting on non-orthogonal input states are investigated, and assessed according to two types of criteria: Transfer of (Shannon) information encoded in the initial states to the copies, and fidelity between the copies and the initial states. Transformations which optimise information transfer for messages encoded in qubits are found. If the message is decoded one symbol at-a-time, information is best copied by a Wootters-Zurek copier.Comment: 14 pages, 3 Figures, REVTeX. Accepted Physical Review A. Corrected minor grammatical error

Universal geometric approach to uncertainty, entropy and information

It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dispersion, localisation, etc, of the ensemble. Remarkably, this unique "ensemble volume" is a simple function of the ensemble entropy, and hence provides a new geometric characterisation of the latter quantity. Applications include unified, volume-based derivations of the Holevo and Shannon bounds in quantum and classical information theory; a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles; a geometric derivation of semi-classical uncertainty relations; a new means for defining classical and quantum localization for arbitrary evolution processes; a geometric interpretation of relative entropy; and a new proposed definition for the spot-size of an optical beam. Advantages of the ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed.Comment: Latex, 38 pages + 2 figures; p(\alpha)->1/|T| in Eq. (72) [Eq. (A10) of published version

Chaos for Liouville probability densities

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time evolution of the Liouville density, the information attaining values that are exponentially larger than the entropy increase that results from averaging over the perturbation. The exponential rate of growth of the ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the map. These findings generalize and extend results obtained for the baker's map [R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.

Zipf law in the popularity distribution of chess openings

We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power-law with an exponent that increases linearly with the game depth, whereas the pooled distribution of all opening weights follows Zipf's law with universal exponent. We propose a simple stochastic process that is able to capture the observed playing statistics and show that the Zipf law arises from the self-similar nature of the game tree of chess. Thus, in the case of hierarchical fragmentation the scaling is truly universal and independent of a particular generating mechanism. Our findings are of relevance in general processes with composite decisions.Comment: 5 pages, 4 figure

Search of low-dimensional magnetics on the basis of structural data: spin-1/2 antiferromagnetic zigzag chain compounds In2VO5, beta-Sr(VOAsO4)2,(NH4,K)2VOF4 and alpha-ZnV3O8

A new technique for searching low-dimensional compounds on the basis of structural data is presented. The sign and strength of all magnetic couplings at distances up to 12 A in five predicted new antiferromagnetic zigzag spin-1/2 chain compounds In2VO5, beta-Sr(VOAsO4)2, (NH4)2VOF4, K2VOF4 and alpha-ZnV3O8 were calculated. It was stated that in the compound In2VO5 zigzag spin chains are frustrated, since the ratio (J2/J1) of competing antiferromagnetic (AF) nearest- (J1) and AF next-to-nearest-neighbour (J2) couplings is equal to 1.68 that exceeds the Majumdar-Ghosh point by 1/2. In other compounds the zigzag spin chains are AF magnetically ordered single chains as value of ratios J2/J1 is close to zero. The interchain couplings were analyzed in detail.Comment: 14 pages, 6 figure, 1 table, minor change