55 research outputs found
Information geometric complexity of a trivariate Gaussian statistical model
We evaluate the information geometric complexity of entropic motion on
low-dimensional Gaussian statistical manifolds in order to quantify how
difficult is making macroscopic predictions about a systems in the presence of
limited information. Specifically, we observe that the complexity of such
entropic inferences not only depends on the amount of available pieces of
information but also on the manner in which such pieces are correlated.
Finally, we uncover that for certain correlational structures, the
impossibility of reaching the most favorable configuration from an entropic
inference viewpoint, seems to lead to an information geometric analog of the
well-known frustration effect that occurs in statistical physics.Comment: 16 pages, 1 figur
Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference
Information geometric techniques and inductive inference methods hold great
promise for solving computational problems of interest in classical and quantum
physics, especially with regard to complexity characterization of dynamical
systems in terms of their probabilistic description on curved statistical
manifolds. In this article, we investigate the possibility of describing the
macroscopic behavior of complex systems in terms of the underlying statistical
structure of their microscopic degrees of freedom by use of statistical
inductive inference and information geometry. We review the Maximum Relative
Entropy (MrE) formalism and the theoretical structure of the information
geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special
focus is devoted to the description of the roles played by the sectional
curvature, the Jacobi field intensity and the information geometrodynamical
entropy (IGE). These quantities serve as powerful information geometric
complexity measures of information-constrained dynamics associated with
arbitrary chaotic and regular systems defined on the statistical manifold.
Finally, the application of such information geometric techniques to several
theoretical models are presented.Comment: 29 page
Information geometric methods for complexity
Research on the use of information geometry (IG) in modern physics has
witnessed significant advances recently. In this review article, we report on
the utilization of IG methods to define measures of complexity in both
classical and, whenever available, quantum physical settings. A paradigmatic
example of a dramatic change in complexity is given by phase transitions (PTs).
Hence we review both global and local aspects of PTs described in terms of the
scalar curvature of the parameter manifold and the components of the metric
tensor, respectively. We also report on the behavior of geodesic paths on the
parameter manifold used to gain insight into the dynamics of PTs. Going
further, we survey measures of complexity arising in the geometric framework.
In particular, we quantify complexity of networks in terms of the Riemannian
volume of the parameter space of a statistical manifold associated with a given
network. We are also concerned with complexity measures that account for the
interactions of a given number of parts of a system that cannot be described in
terms of a smaller number of parts of the system. Finally, we investigate
complexity measures of entropic motion on curved statistical manifolds that
arise from a probabilistic description of physical systems in the presence of
limited information. The Kullback-Leibler divergence, the distance to an
exponential family and volumes of curved parameter manifolds, are examples of
essential IG notions exploited in our discussion of complexity. We conclude by
discussing strengths, limits, and possible future applications of IG methods to
the physics of complexity.Comment: review article, 60 pages, no figure
An information geometric perspective on the complexity of macroscopic predictions arising from incomplete information
Motivated by the presence of deep connections among dynamical equations,
experimental data, physical systems, and statistical modeling, we report on a
series of findings uncovered by the Authors and collaborators during the last
decade within the framework of the so-called Information Geometric Approach to
Chaos (IGAC). The IGAC is a theoretical modeling scheme that combines methods
of information geometry with inductive inference techniques to furnish
probabilistic descriptions of complex systems in presence of limited
information. In addition to relying on curvature and Jacobi field computations,
a suitable indicator of complexity within the IGAC framework is given by the
so-called Information Geometric Entropy (IGE). The IGE is an information
geometric measure of complexity of geodesic paths on curved statistical
manifolds underlying the entropic dynamics of systems specified in terms of
probability distributions. In this manuscript, we discuss several illustrative
examples wherein our modeling scheme is employed to infer macroscopic
predictions when only partial knowledge of the microscopic nature of a given
system is available. Finally, we include comments on the strengths and
weaknesses of the current version of our proposed theoretical scheme in our
concluding remarks.Comment: 26 pages, invited review articl
Bell Diagonal and Werner state generation: entanglement, non-locality, steering and discord on the IBM quantum computer
We propose the first correct special-purpose quantum circuits for preparation
of Bell-diagonal states (BDS), and implement them on the IBM Quantum computer,
characterizing and testing complex aspects of their quantum correlations in the
full parameter space. Among the circuits proposed, one involves only two
quantum bits but requires adapted quantum tomography routines handling
classical bits in parallel. The entire class of Bell-diagonal states is
generated, and a number of characteristic indicators, namely entanglement of
formation, CHSH non-locality, steering and discord, are experimentally
evaluated over the full parameter space and compared with theory. As a
by-product of this work we also find a remarkable general inequality between
"quantum discord" and "asymmetric relative entropy of discord": the former
never exceeds the latter. We also prove that for all BDS the two coincide.Comment: 18 pages, 21 figure
Advances in Fundamental Physics
This Special Issue celebrates the opening of a new section of the journal Foundation: Physical Sciences. Theoretical and experimental studies related to various areas of fundamental physics are presented in this Special Issue. The published papers are related to the following topics: dark matter, electron impact excitation, second flavor of hydrogen atoms, quantum antenna, molecular hydrogen, molecular hydrogen ion, wave pulses, Brans-Dicke theory, hydrogen Rydberg atom, high-frequency laser field, relativistic mean field formalism, nonlocal continuum field theories, parallel universe, charge exchange, van der Waals broadening, greenhouse effect, strange and unipolar electromagnetic pulses, quasicrystals, Wilhelm-Weber’s electromagnetic force law, axions, photoluminescence, neutron stars, gravitational waves, diatomic molecular spectroscopy, information geometric measures of complexity. Among 21 papers published in this Special Issue, there are 5 reviews and 16 original research papers
- …