Quantum properties of classical Fisher information

The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian diffusion, thus providing a measure of robustness. The joint nonclassicality of position and momentum observables is shown to be complementary to their joint robustness in an exact sense.Comment: 16 page

Spectral Simplicity of Apparent Complexity, Part I: The Nondiagonalizable Metadynamics of Prediction

Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type of question---correlation, predictability, predictive cost, observer synchronization, and the like---induces a distinct generator class. Answers are then functions of the class-appropriate transition dynamic. Unfortunately, these dynamics are generically nonnormal, nondiagonalizable, singular, and so on. Tractably analyzing these dynamics relies on adapting the recently introduced meromorphic functional calculus, which specifies the spectral decomposition of functions of nondiagonalizable linear operators, even when the function poles and zeros coincide with the operator's spectrum. Along the way, we establish special properties of the projection operators that demonstrate how they capture the organization of subprocesses within a complex system. Circumventing the spurious infinities of alternative calculi, this leads in the sequel, Part II, to the first closed-form expressions for complexity measures, couched either in terms of the Drazin inverse (negative-one power of a singular operator) or the eigenvalues and projection operators of the appropriate transition dynamic.Comment: 24 pages, 3 figures, 4 tables; current version always at http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt1.ht

Minimal size of a barchan dune

Barchans are dunes of high mobility which have a crescent shape and propagate under conditions of unidirectional wind. However, sand dunes only appear above a critical size, which scales with the saturation distance of the sand flux [P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002); B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B {\bf{28,}} 321 (2002); G. Sauermann, K. Kroy, and H. J. Herrmann, Phys. Rev. E {\bf{64,}} 31305 (2001)]. It has been suggested by P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002) that this flux fetch distance is itself constant. Indeed, this could not explain the proto size of barchan dunes, which often occur in coastal areas of high litoral drift, and the scale of dunes on Mars. In the present work, we show from three dimensional calculations of sand transport that the size and the shape of the minimal barchan dune depend on the wind friction speed and the sand flux on the area between dunes in a field. Our results explain the common appearance of barchans a few tens of centimeter high which are observed along coasts. Furthermore, we find that the rate at which grains enter saltation on Mars is one order of magnitude higher than on Earth, and is relevant to correctly obtain the minimal dune size on Mars.Comment: 11 pages, 10 figure

Information capacity in the weak-signal approximation

We derive an approximate expression for mutual information in a broad class of discrete-time stationary channels with continuous input, under the constraint of vanishing input amplitude or power. The approximation describes the input by its covariance matrix, while the channel properties are described by the Fisher information matrix. This separation of input and channel properties allows us to analyze the optimality conditions in a convenient way. We show that input correlations in memoryless channels do not affect channel capacity since their effect decreases fast with vanishing input amplitude or power. On the other hand, for channels with memory, properly matching the input covariances to the dependence structure of the noise may lead to almost noiseless information transfer, even for intermediate values of the noise correlations. Since many model systems described in mathematical neuroscience and biophysics operate in the high noise regime and weak-signal conditions, we believe, that the described results are of potential interest also to researchers in these areas.Comment: 11 pages, 4 figures; accepted for publication in Physical Review

Information-theoretic interpretation of quantum error-correcting codes

Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while clarifying the differences between classical and quantum codes. More specifically, it is shown how quantum information theory accounts for the fact that "redundant" information can be distributed over quantum bits even though this does not violate the quantum "no-cloning" theorem. Such a remarkable feature, which has no counterpart for classical codes, is related to the property that the ternary mutual entropy vanishes for a tripartite system in a pure state. This information-theoretic description of quantum coding is used to derive the quantum analogue of the Singleton bound on the number of logical bits that can be preserved by a code of fixed length which can recover a given number of errors.Comment: 14 pages RevTeX, 8 Postscript figures. Added appendix. To appear in Phys. Rev.

Diamond (111) surface reconstruction and epitaxial graphene interface

The evolution of the diamond (111) surface as it undergoes reconstruction and subsequent graphene formation is investigated with angle-resolved photoemission spectroscopy, low energy electron diffraction, and complementary density functional theory calculations. The process is examined starting at the C(111)-(2x1) surface reconstruction that occurs following detachment of the surface adatoms at 920 {\deg}C, and continues through to the liberation of the reconstructed surface atoms into a free-standing monolayer of epitaxial graphene at temperatures above 1000 {\deg}C. Our results show that the C(111)-(2x1) surface is metallic as it has electronic states that intersect the Fermi-level. This is in strong agreement with a symmetrically {\pi}-bonded chain model and should contribute to resolving the controversies that exist in the literature surrounding the electronic nature of this surface. The graphene formed at higher temperatures exists above a newly formed C(111)-(2\times1) surface and appears to have little substrate interaction as the Dirac-point is observed at the Fermi-level. Finally, we demonstrate that it is possible to hydrogen terminate the underlying diamond surface by means of plasma processing without removing the graphene layer, forming a graphene-semiconductor interface. This could have particular relevance for doping the graphene formed on the diamond (111)surface via tuneable substrate interactions as a result of changing the terminating species at the diamond-graphene interface by plasma processing.Comment: 10 pages, 4 figure

The photometric properties of a vast stellar substructure in the outskirts of M33

We have surveyed $\sim40$sq.degrees surrounding M33 with CFHT MegaCam in the g and i filters, as part of the Pan-Andromeda Archaeological Survey. Our observations are deep enough to resolve the top 4mags of the red giant branch population in this galaxy. We have previously shown that the disk of M33 is surrounded by a large, irregular, low-surface brightness substructure. Here, we quantify the stellar populations and structure of this feature using the PAndAS data. We show that the stellar populations of this feature are consistent with an old population with $<[Fe/H]>\sim-1.6$dex and an interquartile range in metallicity of $\sim0.5$dex. We construct a surface brightness map of M33 that traces this feature to $\mu_V\simeq33$mags\,arcsec$^{-2}$. At these low surface brightness levels, the structure extends to projected radii of $\sim40$kpc from the center of M33 in both the north-west and south-east quadrants of the galaxy. Overall, the structure has an "S-shaped" appearance that broadly aligns with the orientation of the HI disk warp. We calculate a lower limit to the integrated luminosity of the structure of $-12.7\pm0.5$mags, comparable to a bright dwarf galaxy such as Fornax or AndII and slightly less than $1\$ of the total luminosity of M33. Further, we show that there is tentative evidence for a distortion in the distribution of young stars near the edge of the HI disk that occurs at similar azimuth to the warp in HI. The data also hint at a low-level, extended stellar component at larger radius that may be a M33 halo component. We revisit studies of M33 and its stellar populations in light of these new results, and we discuss possible formation scenarios for the vast stellar structure. Our favored model is that of the tidal disruption of M33 in its orbit around M31.Comment: Accepted for publication in ApJ. 17 figures. ApJ preprint forma

Information Tradeoff Relations for Finite-Strength Quantum Measurements

In this paper we give a new way to quantify the folklore notion that quantum measurements bring a disturbance to the system being measured. We consider two observers who initially assign identical mixed-state density operators to a two-state quantum system. The question we address is to what extent one observer can, by measurement, increase the purity of his density operator without affecting the purity of the other observer's. If there were no restrictions on the first observer's measurements, then he could carry this out trivially by measuring the initial density operator's eigenbasis. If, however, the allowed measurements are those of finite strength---i.e., those measurements strictly within the interior of the convex set of all measurements---then the issue becomes significantly more complex. We find that for a large class of such measurements the first observer's purity increases the most precisely when there is some loss of purity for the second observer. More generally the tradeoff between the two purities, when it exists, forms a monotonic relation. This tradeoff has potential application to quantum state control and feedback.Comment: 15 pages, revtex3, 3 eps figure

Thermodynamic efficiency of information and heat flow

A basic task of information processing is information transfer (flow). Here we study a pair of Brownian particles each coupled to a thermal bath at temperature $T_1$ and $T_2$, respectively. The information flow in such a system is defined via the time-shifted mutual information. The information flow nullifies at equilibrium, and its efficiency is defined as the ratio of flow over the total entropy production in the system. For a stationary state the information flows from higher to lower temperatures, and its the efficiency is bound from above by $\frac{{\rm max}[T_1,T_2]}{|T_1-T_2|}$. This upper bound is imposed by the second law and it quantifies the thermodynamic cost for information flow in the present class of systems. It can be reached in the adiabatic situation, where the particles have widely different characteristic times. The efficiency of heat flow|defined as the heat flow over the total amount of dissipated heat|is limited from above by the same factor. There is a complementarity between heat- and information-flow: the setup which is most efficient for the former is the least efficient for the latter and {\it vice versa}. The above bound for the efficiency can be [transiently] overcome in certain non-stationary situations, but the efficiency is still limited from above. We study yet another measure of information-processing [transfer entropy] proposed in literature. Though this measure does not require any thermodynamic cost, the information flow and transfer entropy are shown to be intimately related for stationary states.Comment: 19 pages, 1 figur