Photon-Number-Splitting versus Cloning Attacks in Practical Implementations of the Bennett-Brassard 1984 protocol for Quantum Cryptography

In practical quantum cryptography, the source sometimes produces multi-photon pulses, thus enabling the eavesdropper Eve to perform the powerful photon-number-splitting (PNS) attack. Recently, it was shown by Curty and Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always the optimal attack when two photons are present: if errors are present in the correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve gains a larger amount of information using another attack based on a 2->3 cloning machine. In this work, we extend this analysis to all distances Alice-Bob. We identify a new incoherent 2->3 cloning attack which performs better than those described before. Using it, we confirm that, in the presence of errors, Eve's better strategy uses 2->3 cloning attacks instead of the PNS. However, this improvement is very small for the implementations of the Bennett-Brassard 1984 (BB84) protocol. Thus, the existence of these new attacks is conceptually interesting but basically does not change the value of the security parameters of BB84. The main results are valid both for Poissonian and sub-Poissonian sources.Comment: 11 pages, 5 figures; "intuitive" formula (31) adde

Near-ideal spontaneous photon sources in silicon quantum photonics

While integrated photonics is a robust platform for quantum information processing, architectures for photonic quantum computing place stringent demands on high quality information carriers. Sources of single photons that are highly indistinguishable and pure, that are either near-deterministic or heralded with high efficiency, and that are suitable for mass-manufacture, have been elusive. Here, we demonstrate on-chip photon sources that simultaneously meet each of these requirements. Our photon sources are fabricated in silicon using mature processes, and exploit a novel dual-mode pump-delayed excitation scheme to engineer the emission of spectrally pure photon pairs through intermodal spontaneous four-wave mixing in low-loss spiralled multi-mode waveguides. We simultaneously measure a spectral purity of $0.9904 \pm 0.0006$, a mutual indistinguishably of $0.987 \pm 0.002$, and $>90\%$ intrinsic heralding efficiency. We measure on-chip quantum interference with a visibility of $0.96 \pm 0.02$ between heralded photons from different sources. These results represent a decisive step for scaling quantum information processing in integrated photonics

Recurrence-based time series analysis by means of complex network methods

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos (2011

Non-linear Redundancy Calibration

For radio interferometric arrays with a sufficient number of redundant spacings the multiplicity of measurements of the same sky visibility can be used to determine both the antenna gains as well as the true visibilities. Many of the earlier approaches to this problem focused on linearized versions of the relation between the measured and the true visibilities. Here we propose to use a standard non-linear minimization algorithm to solve for both the antenna gains as well as the true visibilities. We show through simulations done in the context of the ongoing upgrade to the Ooty Radio Telescope that the non-linear minimization algorithm is fast compared to the earlier approaches. Further, unlike the most straightforward linearized approach, which works with the logarithms of the visibilities and the gains, the non-linear minimization algorithm leads to unbiased solutions. Finally we present error estimates for the estimated gains and visibilities. Monte-Carlo simulations establish that the estimator is indeed statistically efficient, achieving the Cramer-Rao bound.Comment: 9 pages, 5 figures. Accepted for publication in MNRAS. The definitive version will be available at http://mnras.oxfordjournals.or

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure