Key Distillation and the Secret-Bit Fraction

We consider distillation of secret bits from partially secret noisy correlations P_ABE, shared between two honest parties and an eavesdropper. The most studied distillation scenario consists of joint operations on a large number of copies of the distribution (P_ABE)^N, assisted with public communication. Here we consider distillation with only one copy of the distribution, and instead of rates, the 'quality' of the distilled secret bits is optimized, where the 'quality' is quantified by the secret-bit fraction of the result. The secret-bit fraction of a binary distribution is the proportion which constitutes a secret bit between Alice and Bob. With local operations and public communication the maximal extractable secret-bit fraction from a distribution P_ABE is found, and is denoted by Lambda[P_ABE]. This quantity is shown to be nonincreasing under local operations and public communication, and nondecreasing under eavesdropper's local operations: it is a secrecy monotone. It is shown that if Lambda[P_ABE]>1/2 then P_ABE is distillable, thus providing a sufficient condition for distillability. A simple expression for Lambda[P_ABE] is found when the eavesdropper is decoupled, and when the honest parties' information is binary and the local operations are reversible. Intriguingly, for general distributions the (optimal) operation requires local degradation of the data.Comment: 12 page

Evolutionary Inference for Function-valued Traits: Gaussian Process Regression on Phylogenies

Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical model for such data, by combining assumptions from phylogenetics with Gaussian processes. We describe its use as a nonparametric Bayesian prior distribution, both for prediction (placing posterior distributions on ancestral functions) and model selection (comparing rates of evolution across a phylogeny, or identifying the most likely phylogenies consistent with the observed data). Our work is integrative, extending the popular phylogenetic Brownian Motion and Ornstein-Uhlenbeck models to functional data and Bayesian inference, and extending Gaussian Process regression to phylogenies. We provide a brief illustration of the application of our method.Comment: 7 pages, 1 figur

Highly comparative feature-based time-series classification

A highly comparative, feature-based approach to time series classification is introduced that uses an extensive database of algorithms to extract thousands of interpretable features from time series. These features are derived from across the scientific time-series analysis literature, and include summaries of time series in terms of their correlation structure, distribution, entropy, stationarity, scaling properties, and fits to a range of time-series models. After computing thousands of features for each time series in a training set, those that are most informative of the class structure are selected using greedy forward feature selection with a linear classifier. The resulting feature-based classifiers automatically learn the differences between classes using a reduced number of time-series properties, and circumvent the need to calculate distances between time series. Representing time series in this way results in orders of magnitude of dimensionality reduction, allowing the method to perform well on very large datasets containing long time series or time series of different lengths. For many of the datasets studied, classification performance exceeded that of conventional instance-based classifiers, including one nearest neighbor classifiers using Euclidean distances and dynamic time warping and, most importantly, the features selected provide an understanding of the properties of the dataset, insight that can guide further scientific investigation

The Extent of Multi-particle Quantum Non-locality

It is well known that entangled quantum states can be nonlocal: the correlations between local measurements carried out on these states cannot always be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are even more nonlocal than bipartite ones in the sense that nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalises work of Svetlichny and others in which it was shown that a particular class of classical nonlocal models, the ``separable'' models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition.Comment: 10 pages, 2 figures, journal versio

Photon Frequency Mode Matching using Acousto-Optic Frequency Beam Splitters

It is a difficult engineering task to create distinct solid state single photon sources which nonetheless emit photons at the same frequency. It is also hard to create entangled photon pairs from quantum dots. In the spirit of quantum engineering we propose a simple optical circuit which can, in the right circumstances, make frequency distinguishable photons frequency indistinguishable. Our circuit can supply a downstream solution to both problems, opening up a large window of allowed frequency mismatches between physical mechanisms. The only components used are spectrum analysers/prisms and an Acousto-Optic Modulator. We also note that an Acousto-Optic Modulator can be used to obtain Hong-Ou-Mandel two photon interference effects from the frequency distinguishable photons generated by distinct sources.Comment: 4 pages, 4 figure

Explicit tracking of uncertainty increases the power of quantitative rule-of-thumb reasoning in cell biology

"Back-of-the-envelope" or "rule-of-thumb" calculations involving rough estimates of quantities play a central scientific role in developing intuition about the structure and behaviour of physical systems, for example in so-called `Fermi problems' in the physical sciences. Such calculations can be used to powerfully and quantitatively reason about biological systems, particularly at the interface between physics and biology. However, substantial uncertainties are often associated with values in cell biology, and performing calculations without taking this uncertainty into account may limit the extent to which results can be interpreted for a given problem. We present a means to facilitate such calculations where uncertainties are explicitly tracked through the line of reasoning, and introduce a `probabilistic calculator' called Caladis, a web tool freely available at www.caladis.org, designed to perform this tracking. This approach allows users to perform more statistically robust calculations in cell biology despite having uncertain values, and to identify which quantities need to be measured more precisely in order to make confident statements, facilitating efficient experimental design. We illustrate the use of our tool for tracking uncertainty in several example biological calculations, showing that the results yield powerful and interpretable statistics on the quantities of interest. We also demonstrate that the outcomes of calculations may differ from point estimates when uncertainty is accurately tracked. An integral link between Caladis and the Bionumbers repository of biological quantities further facilitates the straightforward location, selection, and use of a wealth of experimental data in cell biological calculations.Comment: 8 pages, 3 figure

Interconversion of Nonlocal Correlations

In this paper we study the correlations that arise when two separated parties perform measurements on systems they hold locally. We restrict ourselves to those correlations with which arbitrarily fast transmission of information is impossible. These correlations are called nonsignaling. We allow the measurements to be chosen from sets of an arbitrary size, but promise that each measurement has only two possible outcomes. We find the structure of this convex set of nonsignaling correlations by characterizing its extreme points. Taking an information-theoretic view, we prove that all of these extreme correlations are interconvertible. This suggests that the simplest extremal nonlocal distribution (called a PR box) might be the basic unit of nonlocality. We also show that this unit of nonlocality is sufficient to simulate all quantum states when measured with two outcome measurements.Comment: 7 pages + appendix, single colum