5,602 research outputs found
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
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