A practical scheme for error control using feedback

We describe a scheme for quantum error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols (for example Ahn et. al, PRA, 65, 042301 (2001)), is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit-flips. We also consider implementation in a solid-state quantum computation architecture and estimate the maximal error rate which could be corrected with current technology.Comment: 12 pages, 3 figures. Minor typographic change

Statistical Communication Theory

Contains reports on one completed research project and one current research project.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 36-039-AMC-03200(E)National Aeronautics and Space Administration (Grant NsG-496)National Science Foundation (Grant GP-2495)National Aeronautics and Space Administration Grant (NsG-334

Neotrusteeship or Mistrusteeship? The Authority Creep Dilemma in United Nations Transitional Administration

State failure poses one of the greatest threats to international peace and security. The collapse of governing institutions breeds civil wars, generates refugee flows, causes enormous civilian suffering, foments instability in neighboring countries, and provides safe havens for transnational criminal and terrorist organizations. As a result, commentators and policymakers have increasingly called for a remedy to the problem of state failure. One of the most compelling arguments is to draw on an old legal institution: international trusteeship by the United Nations (U.N.). This Article argues that while trusteeship may prove effective in managing state failure, it also carries risks. International interventions typically take limited control of the domestic environment of weak countries without absorbing their sovereignty. Trusteeship, in contrast, vests enormous authority and discretion in temporary international administrators, who in turn tend to centralize their power and decision-making in order to meet challenging mission mandates under difficult conditions. This authority creep absorbs sovereignty and in the process risks eroding incentives for leaders of failing states to cooperate with the U.N. Worse, unmitigated authority creep may weaken the political basis for successive international administration and reconstruction efforts. This Article concludes by outlining an alternative system of oversight for U.N. transitional administrators as a means of preserving partial sovereign authority and control for domestic political actors

Statistical Communication Theory

Contains reports on two research projects.Joint Services Electronics Programs (U.S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 28-043-AMC-02536(E)National Aeronautics and Space Administration (Grant NsG-496

Thermodynamics with long-range interactions: from Ising models to black-holes

New methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions. Generically, such systems have entropies which are non-extensive, (do not scale with the size of the system). We show how to calculate the degree of non-extensivity for such a system. We find that a system interacting with a heat reservoir is in a probability distribution of canonical ensembles. The system still possesses a parameter akin to a global temperature, which is constant throughout the substance. There is also a useful quantity which acts like a {\it local temperatures} and it varies throughout the substance. These quantities are closely related to counterparts found in general relativity. A lattice model with long-range spin-spin coupling is studied. This is compared with systems such as those encountered in general relativity, and gravitating systems with Newtonian-type interactions. A long-range lattice model is presented which can be seen as a black-hole analog. One finds that the analog's temperature and entropy have many properties which are found in black-holes. Finally, the entropy scaling behavior of a gravitating perfect fluid of constant density is calculated. For weak interactions, the entropy scales like the volume of the system. As the interactions become stronger, the entropy becomes higher near the surface of the system, and becomes more area-scaling.Comment: Corrects some typos found in published version. Title changed 22 pages, 2 figure

Spectral Simplicity of Apparent Complexity, Part II: Exact Complexities and Complexity Spectra

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior. Using the resulting spectral decomposition, we derive closed-form expressions for correlation functions, finite-length Shannon entropy-rate approximates, asymptotic entropy rate, excess entropy, transient information, transient and asymptotic state uncertainty, and synchronization information of stochastic processes generated by finite-state hidden Markov models. This introduces analytical tractability to investigating information processing in discrete-event stochastic processes, symbolic dynamics, and chaotic dynamical systems. Comparisons reveal mathematical similarities between complexity measures originally thought to capture distinct informational and computational properties. We also introduce a new kind of spectral analysis via coronal spectrograms and the frequency-dependent spectra of past-future mutual information. We analyze a number of examples to illustrate the methods, emphasizing processes with multivariate dependencies beyond pairwise correlation. An appendix presents spectral decomposition calculations for one example in full detail.Comment: 27 pages, 12 figures, 2 tables; most recent version at http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt2.ht

Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects

The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signal-to-noise ratios (SNR), or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. In this paper I discuss these pitfalls; show how they occur, even for relatively strong signals, with a commonly used template family for binary-inspiral waveforms; and describe practical recipes to recognize them and cope with them. Specifically, I answer the following questions: (i) What is the significance of (quasi-)singular Fisher matrices, and how must we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signal-to-noise ratio high enough to believe the Fisher-matrix result? In addition, I provide general expressions for the higher-order, beyond--Fisher-matrix terms in the 1/SNR expansions for the expected parameter accuracies.Comment: 24 pages, 3 figures, previously known as "A User Manual for the Fisher Information Matrix"; final, corrected PRD versio

Phase transition in the Jarzynski estimator of free energy differences

The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in terms of the change in behavior of the Jarzynski estimator of equilibrium free energy differences from nonequilibrium work measurements. Given a fixed number of measurements, the Jarzynski estimator is unbiased for sufficiently small systems. In these systems, the directionality of time is poorly defined and configurations that dominate the empirical average, but which are in fact typical of the reverse process, are sufficiently well sampled. As the system size increases the arrow of time becomes better defined. The dominant atypical fluctuations become rare and eventually cannot be sampled with the limited resources that are available. Asymptotically, only typical work values are measured. The Jarzynski estimator becomes maximally biased and approaches the exponential of minus the average work, which is the result that is expected from standard macroscopic thermodynamics. In the proper scaling limit, this regime change can be described in terms of a phase transition in variants of the random energy model (REM). This correspondence is explicitly demonstrated in several examples of physical interest: near-equilibrium processes in which the work distribution is Gaussian, the sudden compression of an ideal gas and adiabatic quasi-static volume changes in a dilute real gas.Comment: 29 pages, 5 figures, accepted for publication in Physical Review E (2012

Statistical Communication Theory

Contains reports on three completed research projects and reports on two current research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 36-039-AMC-03200(E)National Aeronautics and Space Administration (Grant NsG-496)National Science Foundation (Grant GK-835)National Aeronautics and Space Administration Grant (NsG-334

Notes on the integration of numerical relativity waveforms

A primary goal of numerical relativity is to provide estimates of the wave strain, $h$, from strong gravitational wave sources, to be used in detector templates. The simulations, however, typically measure waves in terms of the Weyl curvature component, $\psi_4$. Assuming Bondi gauge, transforming to the strain $h$ reduces to integration of $\psi_4$ twice in time. Integrations performed in either the time or frequency domain, however, lead to secular non-linear drifts in the resulting strain $h$. These non-linear drifts are not explained by the two unknown integration constants which can at most result in linear drifts. We identify a number of fundamental difficulties which can arise from integrating finite length, discretely sampled and noisy data streams. These issues are an artifact of post-processing data. They are independent of the characteristics of the original simulation, such as gauge or numerical method used. We suggest, however, a simple procedure for integrating numerical waveforms in the frequency domain, which is effective at strongly reducing spurious secular non-linear drifts in the resulting strain.Comment: 23 pages, 10 figures, matches final published versio