Generalized decoding, effective channels, and simplified security proofs in quantum key distribution

Prepare and measure quantum key distribution protocols can be decomposed into two basic steps: delivery of the signals over a quantum channel and distillation of a secret key from the signal and measurement records by classical processing and public communication. Here we formalize the distillation process for a general protocol in a purely quantum-mechanical framework and demonstrate that it can be viewed as creating an ``effective'' quantum channel between the legitimate users Alice and Bob. The process of secret key generation can then be viewed as entanglement distribution using this channel, which enables application of entanglement-based security proofs to essentially any prepare and measure protocol. To ensure secrecy of the key, Alice and Bob must be able to estimate the channel noise from errors in the key, and we further show how symmetries of the distillation process simplify this task. Applying this method, we prove the security of several key distribution protocols based on equiangular spherical codes.Comment: 9.1 pages REVTeX. (v3): published version. (v2): revised for improved presentation; content unchange

Analyzing Finite-length Protograph-based Spatially Coupled LDPC Codes

The peeling decoding for spatially coupled low-density parity-check (SC-LDPC) codes is analyzed for a binary erasure channel. An analytical calculation of the mean evolution of degree-one check nodes of protograph-based SC-LDPC codes is given and an estimate for the covariance evolution of degree-one check nodes is proposed in the stable decoding phase where the decoding wave propagates along the chain of coupled codes. Both results are verified numerically. Protograph-based SC-LDPC codes turn out to have a more robust behavior than unstructured random SC-LDPC codes. Using the analytically calculated parameters, the finite- length scaling laws for these constructions are given and verified by numerical simulations.Comment: 5 pages, 6 figures, submitted to ISIT 201

Analytic Solutions of Ultra-High Energy Cosmic Ray Nuclei Revisited

The chemical composition of ultra-high energy cosmic rays is a key question in particle astrophysics. The measured composition, inferred from the elongation rates of cosmic ray showers, looks in general very different from the initial source composition: resonant photo-disintegration in the cosmic radiation background proceeds rapidly at the highest energies and the initial composition quickly becomes lighter during propagation. For a statistical analysis of continuously improving cosmic ray data it is desirable to know the secondary spectra as precisely as possible. Here, we discuss exact analytic solutions of the evolution equation of ultra-high energy cosmic ray nuclei. We introduce a diagrammatic formalism that leads to a systematic analytic expansion of the exact solution in terms of second order effects of the propagation. We show how the first order corrections of this expansion can improve the predictions of secondary spectra in a semi-analytical treatment.Comment: 10 figures, 1 tabl

Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for DCTs and DSTs

This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives the algorithms by stepwise decomposition of the associated signal models, or polynomial algebras. This decomposition is based on two generic methods or algebraic principles that generalize the well-known Cooley-Tukey FFT and make the algorithms' derivations concise and transparent. Application to the 16 discrete cosine and sine transforms yields a large class of fast algorithms, many of which have not been found before.Comment: 31 pages, more information at http://www.ece.cmu.edu/~smar

Transient localized wave patterns and their application to migraine

Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic forms (shape, size, duration) in a canonical reaction-diffusion model with mean field inhibition. The patterns are formed by a ghost near a saddle-node bifurcation in which a stable traveling wave (node) collides with its critical nucleation mass (saddle). Similar patterns have been observed with fMRI in migraine. Our results support the controversial idea that waves of cortical spreading depression (SD) have a causal relationship with the headache phase in migraine and therefore occur not only in migraine with aura (MA) but also in migraine without aura (MO), i.e., in the two major migraine subforms. We suggest a congruence between the prevalence of MO and MA with the statistical properties of the traveling waves' forms, according to which (i) activation of nociceptive mechanisms relevant for headache is dependent upon a sufficiently large instantaneous affected cortical area anti-correlated to both SD duration and total affected cortical area such that headache would be less severe in MA than in MO (ii) the incidence of MA is reflected in the distance to the saddle-node bifurcation, and (iii) the contested notion of MO attacks with silent aura is resolved. We briefly discuss model-based control and means by which neuromodulation techniques may affect pathways of pain formation.Comment: 14 pages, 11 figure

Dynamics of the critical Casimir force for a conserved order parameter after a critical quench

Fluctuation-induced forces occur generically when long-ranged correlations (e.g., in fluids) are confined by external bodies. In classical systems, such correlations require specific conditions, e.g., a medium close to a critical point. On the other hand, long-ranged correlations appear more commonly in certain non-equilibrium systems with conservation laws. Consequently, a variety of non-equilibrium fluctuation phenomena, including fluctuation-induced forces, have been discovered and explored recently. Here, we address a long-standing problem of non-equilibrium critical Casimir forces emerging after a quench to the critical point in a confined fluid with order-parameter-conserving dynamics and non-symmetry-breaking boundary conditions. The interplay of inherent (critical) fluctuations and dynamical non-local effects (due to density conservation) gives rise to striking features, including correlation functions and forces exhibiting oscillatory time-dependences. Complex transient regimes arise, depending on initial conditions and the geometry of the confinement. Our findings pave the way for exploring a wealth of non-equilibrium processes in critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In certain regimes, our results are applicable to active matter.Comment: 38 pages, 11 figure

Is There a "Dead-Anyway" Effect in Willingness to Pay for Risk Reduction?

In einem neueren Beitrag diskutieren Pratt and Zeckhauser (JPE, 1996), welches Maß der marginalen Zahlungsbereitschaft (WTP) von Individuen für die Reduktion ihrer Sterbewahrscheinlichkeit bei öffentlichen Entscheidungen über gefahrenerhebliche Projekte verwendet werden sollte. Sie schlagen vor, die gemessene WTP um den so genannten "Dead-anyway"-Effekt zu berichtigen, der besagt, dass die WTP mit dem Ausgangswert des Risikos zunimmt, dem das befragte Individuum ausgesetzt ist. Dieser Effekt beruht allerdings auf der Abwesenheit vollkommener Märkte für bedingte Güter. Wir diskutieren zunächst die theoretischen Grundlagen des "Dead-anyway"-Effekts und schlagen dann einen neuen empirischen Test mittels der Beziehung zwischen Vermögen, Sterberisiko und Lebenszufriedenheit vor. Eine Anwendung des Tests an Hand zweier Sätze von Umfragedaten aus Deutschland und Australien ergibt keine Bestätigung für den von Pratt und Zeckhauser behaupteten Effekt. In a recent paper, Pratt and Zeckhauser (JPE, 1996) discuss the measure of individuals' willingness to pay (WTP) for the reduction of risks to their lives which should be used for public decisions on risk-reducing projects. They suggest to correct observed WTP for the "dead-anyway" effect, which says that WTP increases with the level of risk to which the individual is exposed - an effect which is due to the imperfection of contingent-claims markets. We first discuss the theoretical foundations of the asserted effect and then propose a new empirical test based on the relationship between wealth, life satisfaction and exposure to risk of dying. Application of the test using two sets of survey data from Germany and Australia.yields no support for the asserted dead-anyway effect.value of statistical life, mortality risk, contingent-claims markets

Copayments for Ambulatory Care in Germany: A Natural Experiment Using a Difference-in-Difference Approach

In response to increasing health expenditures and a high number of physician visits, the German government introduced a copayment for ambulatory care in 2004 for individuals with statutory health insurance (SHI). Because persons with private insurance were exempt from the copayments, this health care reform can be regarded as a natural experiment. We used a difference-in-difference approach to examine whether the new copayment effectively reduced the overall demand for physician visits and to explore whether it acted as a deterrent to vulnerable groups, such as those with low income or chronic conditions. We found that there was no significant reduction in the number of physician visits among SHI members compared to our control group. At the same time, we did not observe a deterrent effect among vulnerable individuals. Thus, the copayment has failed to reduce the demand for physician visits. It is likely that this result is due to the design of the copayment scheme, as the copayment is low and is paid only for the first physician visit per quarter.Copayments, ambulatory care, difference-in-difference, count data, zeroinflated-model, SOEP

Coupled Electron Ion Monte Carlo Calculations of Atomic Hydrogen

We present a new Monte Carlo method which couples Path Integral for finite temperature protons with Quantum Monte Carlo for ground state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. This method fills the gap between high temperature electron-proton Path Integral and ground state Diffusion Monte Carlo methods. Our data exhibit more structure and higher melting temperatures of the proton crystal than Car-Parrinello Molecular Dynamics results using LDA. We further discuss the quantum motion of the protons and the zero temperature limit