Showing papers on "Coherent information published in 1992"

Information In Dynamics

Abstract: The historical search for the fundamental meaning of thermodynamic entropy lead to the discovery of the connection between entropy and information about microscopic dynamics, which in turn motivated the development of the theory of information in communications. In this paper I will review how information theory can profitably be applied back to its roots in dynamics in order to characterize the essential properties of a measured time series. Entropy was introduced in the familiar modern form (dS = SQ/T) by Clausius in 1854, building on work by Carnot (1824) and Kelvin (-1850) to understand the nature of heat and irreversability in thermodynamic systems.'I2 Boltzmann was dedicated to understanding the microscopic meaning of this macroscopic entropy; influenced by Maxwell's kinetic theory of gases (-1860) he introduced the relationship H = f(r,p,t)log f(r,p,t)d3rd3p (where f is the velocity distribution in a gas) in 1872, and then the more general form S = k log W (where W is the number of available states) around 1877. In 1871 Maxwell created his dem~n,~ which appeared to violate the second law of thermodynamics by intelligent action. Szilard, in 1929, made the significant step of considering a one-molecule gas that could be on either side of a partition; this introducing the idea of a binary bit of information (which side of the partition the molecule is in) and of using entropy to measure inf~rmation.~ Although Sxilard missed the crucial role of erase in explaining the demon's (mis)behavior (this was first recognized by Landauer5), he had laid the foundation for the development of both reversible computation6 and of information the~ry.~ In 1948 Shannon applied entropy to measure the information content in an arbitrary message, independent of its physical origin, and was thereby able to solve significant outstanding communications problems such as the maximum rate at which a message can be sent through a channel. Information theory has since flourished in engineering practice.8 The study of ergodic systems has both benefited from, and contributed to, information the~ry.~ More recently, Shaw pointed out the connection between information and dissipative dynamics," and Fraser extended this to develop a framework that I will describe here for characterizing the structure in time series produced by non-linear systems.l' Although a dynamical system's global structure can perform nontrivial computations,12i13 analyzing the information evolution associated with the much simpler local behavior is sufficient to answer deep questions about the complexity and predictability of a system. In this paper I will will explain how to understand and measure such information. As well as being quite useful in practice, this application of information theory back to its roots in dynamics provides a simple but clear example of the physical meaning of inf~rniation.'~ Assume that a physical system is described by a state vector 5 and governing equations d21dt = f (5) (or &+I = f(&)). This need not imply that the system is finite-dimensional; the underlying governing equations may be infinite-dimensional partial differential equations which reduce to a finite-dimensional mode expansion due to dissipation. Let y(g(t)) be a scalar experimentally-accessible quantity that is a function of the state of the system (such as the temperature or velocity at a point in a fluid convection cell, or the concentration of a particular species in a chemical reaction). The goal is to learn as much as possible about the underlying system given only the time series y(t). The necessary connection between the observed time series and its physical origin is provided by state-space reconstruction.15- 's Construct a new vector out of lagged copies of the observable and the dimension d are parameters that will be discussed shortly. If d is large enough, thzn for almost any choice of the governing equations f, the observable u(Z), and the time delay T, the motion of the zt 4 = (yt, ytbT,. . ., yt.-(d-.llT), where the time lag T

Physical Information Theory Part II: Quantum Systems

Abstract: The concept of information (by Shannon) is generalized for quantum statistical ensembles, and the consistent quantum-theoretical form of the entropy defect principle is obtained. The efect of the irreversiblility of quantummechanical measurements on information transmission is analyzed. For the ensemble of two pure quantum states, the optimal measurement procedure is found in the explicit form.

Physical Information Theory Part I. Quasiclassical Systems

Abstract: A short review of the development of the physical information theory is presented. The entropy defect principle is formulated for quasiclassical systems. The concept of ideal physical information channels is iintroduced. It is shown that information properties of such a channel with independent additive noise can be ontained from the thermodynamic description of the physical system that transmits information. BrillouinS conjecture of minimum enerrgy per unit of information is proved for this type of channels.

Storage And Retrieval Of Quantum Information

Abstract: Information encoded in non-orthogonal quantum states cannot be duplicated, nor amplified, and in general at is only partly recoverable. The most efficient way of retrieving it is not a direct uquantum measurement” (as defined by von Neumann), but an indirect method similar to heterodyne detection in communications engineering. The mathematical representation of this process requires the introduction of a positive operator valued measure. The optimization of these measures is not yet fully undersiood. An interesting and potentially important application of quantum information is its use an cryptography.

Uncertainty, entropy, and mutual information for quantum states

Abstract: The quantity mutual information is introduced as a good measure of the quantum-mechanical uncertainty of a state. The mutual information is the measured value of entropy for both discrete and continuous variables, with the resolution of the measuring device as a constraint. The mutual information is calculated for coherent states and squeezed states; the values of the variables before and after the measurement are assumed to be correlated Gaussian, with correlation coefficient γ. It is found that the information increases or decreases from the corresponding coherent state value, depending on γ.

The Two Extremes Of Information In Quantum Mechanics

Abstract: In the problem of estimating the amount of information one can extract from a quantum system, the entropy S of the system is known to play a special role: it is an upper bound on the accessible information. This paper calls attention to another property of quantum systems, called Q, which appears to play an analogous role in defining a lower bound on the accessible information. Some parallels between S and Q are noted.

Angular Discretization Errors in Transport Theory: An Information-Based Approach

Abstract: Elements of the information-based complexity theory are computed for several types of information and associated algorithms for angular approximations in the setting of a on-dimensional model problem. For point-evaluation information, the local and global radii of information are computed, a (trivial) optimal algorithm is determined, and the local and global error of a discrete ordinates algorithm are shown to be infinite. For average cone-integral information, the local and global radii of information are computed, the local and global error tends to zero as the underlying partition is indefinitely refined. A central algorithm for such information and an optimal partition (of given cardinality) are described. It is further shown that the analytic first-collision source method has zero error (for the purely absorbing model problem). Implications of the restricted problem domains suitable for the various types of information are discussed.

Information Theory and Quantum Wave Functions

Abstract: A new scheme for the reconstruction and approximation of quantum wave functions is derived within the context of Information Theory. The method is applied to the inference of the energy spectra and the pertinent eigenstates of special hamiltonians from incomplete information concerning the system’s ground state, and to the development of an approximation for the ground state of a superconducting many-fermion model. A substantial improvement over standard and projected BCS approximations is obtained, especially in transitional regions.

Some information applications of lasers

Abstract: Specific laser applications in information systems for two important cases-nonlinear digital computing optical systems and coherent information laser systems-are described. Some new results obtained at the S. I. Vavilov State Optical Institute are presented. The state-of-the-art and possible applications of feedback nonlinear optical systems for digital parallel data processing are discussed. New possibilities produced by employing high-quality laser radiation in transverse distributed wide-aperture bistable systems are presented, and the main properties of such systems (spatial hysteresis, diffraction autosolitons, and switching waves) are discussed. A discussion of coherent information laser systems is included. The results obtained with high-performance neodimium-doped lasers are reviewed. The amplification of single-frequency cw laser radiation in a pulsed solid state amplifier is discussed. Finally, some theoretical and experimental results concerning the frequency purity of amplified signals are presented.