New multiplicativity results for qubit maps

Let $\Phi$ be a trace-preserving, positivity-preserving (but not necessarily completely positive) linear map on the algebra of complex $2 \times 2$ matrices, and let $\Omega$ be any finite-dimensional completely positive map. For $p=2$ and $p \geq 4$, we prove that the maximal $p$-norm of the product map \Phi \ot \Omega is the product of the maximal $p$-norms of $\Phi$ and $\Omega$. Restricting $\Phi$ to the class of completely positive maps, this settles the multiplicativity question for all qubit channels in the range of values $p \geq 4$.Comment: 14 pages; original proof simplified by using Gorini and Sudarshan's classification of extreme affine maps on R^

Improving CMB non-Gaussianity estimators using tracers of local structure

Local non-Gaussianity causes correlations between large scale perturbation modes and the small scale power. The large-scale CMB signal has contributions from the integrated Sachs Wolfe (ISW) effect, which does not correlate with the small scale power. If this ISW contribution can be removed, the sensitivity to local non-Gaussianity is improved. Gravitational lensing and galaxy counts can be used to trace the ISW contribution; in particular we show that the CMB lensing potential is highly correlated with the ISW signal. We construct a nearly-optimal estimator for the local non-Gaussianity parameter \fnl and investigate to what extent we can use this to decrease the variance on {\fnl}. We show that the variance can be decreased by up to $20\%$ at Planck sensitivity using galaxy counts. CMB lensing is a good bias-independent ISW tracer for future more sensitive observations, though the fractional decrease in variance is small if good polarization data is also available.Comment: 8 pages, 3 figures. Comments welcom

Molecular Beams

Contains a report on a research project.Lincoln Laboratory (Purchase Order B-00306)United States ArmyUnited States NavyUnited States Air Force (Contract AF19(604)-5200

Verifying termination and error-freedom of logic programs with block declarations

We present verification methods for logic programs with delay declarations. The verified properties are termination and freedom from errors related to built-ins. Concerning termination, we present two approaches. The first approach tries to eliminate the well-known problem of speculative output bindings. The second approach is based on identifying the predicates for which the textual position of an atom using this predicate is irrelevant with respect to termination. Three features are distinctive of this work: it allows for predicates to be used in several modes; it shows that block declarations, which are a very simple delay construct, are sufficient to ensure the desired properties; it takes the selection rule into account, assuming it to be as in most Prolog implementations. The methods can be used to verify existing programs and assist in writing new programs

Electron Optics

Contains research objectives and summary of research.Joint Services Electronics Program (Contract DAAB07 -71 -C-0300

Energetic solar proton versus terrestrially trapped proton fluxes for the active years 1977 - 1983

Ratios of solar to trapped proton fluences were computed for circular-orbit, geocentric space missions to be flown during the active phase of the next solar cycle (1977-1983). The ratios are presented as functions of orbit altitude and inclination, mission duration, proton energy threshold, and the chance the mission planner is willing to take that the actually encountered solar proton fluence will exceed the design fluence provided by the statistical solar proton model. It is shown that the ratio is most sensitively dependent on orbit altitude and inclination, with trapped protons dominant for low inclination, low and mid altitude orbits and for high inclination, mid altitude orbits. Conversely, solar protons are dominant for high inclination, low altitude orbits, and for low and high inclination, high altitude orbits

Analysis of distortion data from TF30-P-3 mixed compression inlet test

A program was conducted to reduce and analyze inlet and engine data obtained during testing of a TF30-P-3 engine operating behind a mixed compression inlet. Previously developed distortion analysis techniques were applied to the data to assist in the development of a new distortion methodology. Instantaneous distortion techniques were refined as part of the distortion methodology development. A technique for estimating maximum levels of instantaneous distortion from steady state and average turbulence data was also developed as part of the program

Proof of Luck: an Efficient Blockchain Consensus Protocol

In the paper, we present designs for multiple blockchain consensus primitives and a novel blockchain system, all based on the use of trusted execution environments (TEEs), such as Intel SGX-enabled CPUs. First, we show how using TEEs for existing proof of work schemes can make mining equitably distributed by preventing the use of ASICs. Next, we extend the design with proof of time and proof of ownership consensus primitives to make mining energy- and time-efficient. Further improving on these designs, we present a blockchain using a proof of luck consensus protocol. Our proof of luck blockchain uses a TEE platform's random number generation to choose a consensus leader, which offers low-latency transaction validation, deterministic confirmation time, negligible energy consumption, and equitably distributed mining. Lastly, we discuss a potential protection against up to a constant number of compromised TEEs.Comment: SysTEX '16, December 12-16, 2016, Trento, Ital

Entangled inputs cannot make imperfect quantum channels perfect

Entangled inputs can enhance the capacity of quantum channels, this being one of the consequences of the celebrated result showing the non-additivity of several quantities relevant for quantum information science. In this work, we answer the converse question (whether entangled inputs can ever render noisy quantum channels have maximum capacity) to the negative: No sophisticated entangled input of any quantum channel can ever enhance the capacity to the maximum possible value; a result that holds true for all channels both for the classical as well as the quantum capacity. This result can hence be seen as a bound as to how "non-additive quantum information can be". As a main result, we find first practical and remarkably simple computable single-shot bounds to capacities, related to entanglement measures. As examples, we discuss the qubit amplitude damping and identify the first meaningful bound for its classical capacity.Comment: 5 pages, 2 figures, an error in the argument on the quantum capacity corrected, version to be published in the Physical Review Letter

Time-Separable Preference and Intertemporal-Substitution Models of Business Cycles

Time-separability of utility means that past work and consumption do not influence current and future tastes. This form of preferences does not restrict the size of intertemporal-substitution effects--notably, we can still have a strong response of labor supply to temporary changes in wages. However, there are important constraints on the relative responses of leisure and consumption to changes in relative-price and in permanent income. When the usual aggregation is permissible, time-separability has some important implications for equilibrium theories of the business cycle. Neglecting investment, we, find that changes in perceptions about the future -- which night appear currently as income effects -- have no influence on current equilibrium output. With investment included, no combination of income effects and shifts to the perceived profitability of investment will yield positive co-movements of output, employment, investment and consumption. Therefore, misperceived monetary disturbances or other sources of changed beliefs about the future cannot be used to generate empirically recognizable business cycles. Some richer specifications of intertemporal production opportunities may eventually yield more satisfactory answers. Because of the positive correlation between cyclical movements of consumption and work, equilibrium theories with time-separable preferences inevitably predict a procyclical behavior for the real wage rate, arising from shifts to labor's marginal product. Empirically, we regard the cyclical behavior of real wages as an open question. Aside from analyzing autonomous real shocks to productivity, we suggest that such shifts may occur as firms vary their capital utilization in response to intertemporal relative prices. However, we still lack some parts of a complete theory.