Fundamental finite key limits for information reconciliation in quantum key distribution

The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during one-way information reconciliation is flawed and we propose an improved estimate.

Quantum communications in optical networks

La posibilidad de utilizar sistemas cuánticos para procesar y transmitir información ha impulsado la aparición de tecnologías de información cuántica, p. ej., distribución cuántica de claves. Aunque prometedoras, su uso fuera del laboratorio es actualmente demasiado costoso y complicado. En este trabajo mostramos como utilizarlas en redes ópticas de telecomunicaciones. Al utilizar una infraestructura existente y pervasiva, y compartirla con otras señales, tanto clásicas como cuánticas, el coste se reduce drásticamente y llega a un mayor público. Comenzamos integrando señales cuánticas en los tipos más utilizados de redes ópticas pasivas, por su simplicidad y alcance a usuarios finales. Luego ampliamos este estudio, proponiendo un diseño de red óptica metropolitana basado en la división en longitud de onda para multiplexar y direccionar las señales. Verificamos su funcionamiento con un prototipo. Posteriormente, estudiamos la distribución de pares de fotones entrelazados entre los usuarios de dicha red con el objetivo de abarcar más tecnologías. Para ampliar la capacidad de usuarios, rediseñamos la red troncal, cambiando tanto la topología como la tecnología utilizada en los nodos. El resultado es una red metropolitana cuántica que escala a cualquier cantidad de usuarios, a costa de una mayor complejidad y coste. Finalmente, tratamos el problema de la limitación en distancia. La solución propuesta está basada en codificación de red y permite, mediante el uso de varios caminos y nodos, modular la cantidad de información que tiene cada nodo, y así, la confianza depositada en él. ABSTRACT The potential use of quantum systems to process and transmit information has impulsed the emergence of quantum information technologies such as quantum key distribution. Despite looking promising, their use out of the laboratory is limited since they are a very delicate technology due to the need of working at the single quantum level. In this work we show how to use them in optical telecommunication networks. Using an existing infrastructure and sharing it with other signals, both quantum and conventional, reduces dramatically the cost and allows to reach a large group of users. In this work, we will first integrate quantum signals in the most common passive optical networks, for their simplicity and reach to final users. Then, we extend this study by proposing a quantum metropolitan optical network based on wavelength-division multiplexing and wavelengthaddressing, verifying its operation mode in a testbed. Later, we study the distribution of entangled photon-pairs between the users of the network with the objective of covering as much different technologies as possible. We further explore other network architectures, changing the topology and the technology used at the nodes. The resulting network scales better at the cost of a more complex and expensive infrastructure. Finally, we tackle the distance limitation problem of quantum communications. The solution offered is based on networkcoding and allows, using multiple paths and nodes, to modulate the information leaked to each node, and thus, the degree of trust placed in them.

Entanglement Distribution in Quantum Metropolitan Optical Networks

The ability to generate entangled photon-pairs over a broad wavelength range opens the door to the simultaneous distribution of entanglement to multiple users of a network using a single source and wavelength-division multiplexing technologies. Here we show the design of a metropolitan optical network made of tree-type access networks where entangled photon-pairs are distributed to any pair of users, independently of their location. The resulting network improves the reach, number of users and capabilities of existing proposals. Moreover, it is made up of typical commercial components and uses the existing infrastructure, which allows for moderate deployment costs. Finally, we develop a channel plan and a network design that allow direct optical communications, quantum and classical, between any pair of users. Therefore, multiple quantum information technologies can make use of this network.

Demystifying the information reconciliation protocol cascade

Cascade is an information reconciliation protocol proposed in the context of secret key agreement in quantum cryptography. This protocol allows removing discrepancies in two partially correlated sequences that belong to distant parties, connected through a public noiseless channel. It is highly interactive, thus requiring a large number of channel communications between the parties to proceed and, although its efficiency is not optimal, it has become the de-facto standard for practical implementations of information reconciliation in quantum key distribution. The aim of this work is to analyze the performance of Cascade, to discuss its strengths, weaknesses and optimization possibilities, comparing with some of the modified versions that have been proposed in the literature. When looking at all design trade-offs, a new view emerges that allows to put forward a number of guidelines and propose near optimal parameters for the practical implementation of Cascade improving performance significantly in comparison with all previous proposals.

Integration of quantum key distribution in metropolitan area networks

The deployment of Quantum Key Distribution forces the development of QKD-links to be operated in current and next-generation photonic metro-access networks. These highly heterogeneous architectures determine the conditions QKD-links need to be optimized for.

Uniformly Reweighted Belief Propagation: A Factor Graph Approach

Tree-reweighted belief propagation is a message passing method that has certain advantages compared to traditional belief propagation (BP). However, it fails to outperform BP in a consistent manner, does not lend itself well to distributed implementation, and has not been applied to distributions with higher-order interactions. We propose a method called uniformly-reweighted belief propagation that mitigates these drawbacks. After having shown in previous works that this method can substantially outperform BP in distributed inference with pairwise interaction models, in this paper we extend it to higher-order interactions and apply it to LDPC decoding, leading performance gains over BP.

Two way clustering of Microarray Data using a Hybrid Approach

The Microarray technique is rather powerful, as it allows to test up thousands of genes at a time, but this produces an overwhelming set of data files containing huge amounts of data, which is quite difficult to pre-process, separate, classify and correlate for interesting conclusions to be extracted. Modern machine learning, data mining and clustering techniques based on information theory, are needed to read and interpret the information contents buried in those large data sets. Independent Component Analysis method can be used to correct the data affected by corruption processes or to filter the uncorrectable one and then clustering methods can group similar genes or classify samples. In this paper a hybrid approach is used to obtain a two way unsupervised clustering for a corrected microarray data.

Blind reconiliation

Information reconciliation is a crucial procedure in the classical post-processing of quantum key distribution (QKD). Poor reconciliation e?ciency, revealing more information than strictly needed, may compromise the maximum attainable distance, while poor performance of the algorithm limits the practical throughput in a QKD device. Historically, reconciliation has been mainly done using close to minimal information disclosure but heavily interactive procedures, like Cascade, or using less e?cient but also less interactive ?just one message is exchanged? procedures, like the ones based in low-density parity-check (LDPC) codes. The price to pay in the LDPC case is that good e?ciency is only attained for very long codes and in a very narrow range centered around the quantum bit error rate (QBER) that the code was designed to reconcile, thus forcing to have several codes if a broad range of QBER needs to be catered for. Real world implementations of these methods are thus very demanding, either on computational or communication resources or both, to the extent that the last generation of GHz clocked QKD systems are ?nding a bottleneck in the classical part. In order to produce compact, high performance and reliable QKD systems it would be highly desirable to remove these problems. Here we analyse the use of short-length LDPC codes in the information reconciliation context using a low interactivity, blind, protocol that avoids an a priori error rate estimation. We demonstrate that 2×103 bits length LDPC codes are suitable for blind reconciliation. Such codes are of high interest in practice, since they can be used for hardware implementations with very high throughput.

Feature selection in the reconstruction of complex network representations of spectral data

Complex networks have been extensively used in the last decade to characterize and analyze complex systems, and they have been recently proposed as a novel instrument for the analysis of spectra extracted from biological samples. Yet, the high number of measurements composing spectra, and the consequent high computational cost, make a direct network analysis unfeasible. We here present a comparative analysis of three customary feature selection algorithms, including the binning of spectral data and the use of information theory metrics. Such algorithms are compared by assessing the score obtained in a classification task, where healthy subjects and people suffering from different types of cancers should be discriminated. Results indicate that a feature selection strategy based on Mutual Information outperforms the more classical data binning, while allowing a reduction of the dimensionality of the data set in two orders of magnitude

Analysis of spontaneous MEG activity in mild cognitive impairment and Alzheimer's disease using spectral entropies and statistical complexity measures

Alzheimer's disease (AD) is the most common cause of dementia. Over the last few years, a considerable effort has been devoted to exploring new biomarkers. Nevertheless, a better understanding of brain dynamics is still required to optimize therapeutic strategies. In this regard, the characterization of mild cognitive impairment (MCI) is crucial, due to the high conversion rate from MCI to AD. However, only a few studies have focused on the analysis of magnetoencephalographic (MEG) rhythms to characterize AD and MCI. In this study, we assess the ability of several parameters derived from information theory to describe spontaneous MEG activity from 36 AD patients, 18 MCI subjects and 26 controls. Three entropies (Shannon, Tsallis and Rényi entropies), one disequilibrium measure (based on Euclidean distance ED) and three statistical complexities (based on Lopez Ruiz–Mancini–Calbet complexity LMC) were used to estimate the irregularity and statistical complexity of MEG activity. Statistically significant differences between AD patients and controls were obtained with all parameters (p < 0.01). In addition, statistically significant differences between MCI subjects and controls were achieved by ED and LMC (p < 0.05). In order to assess the diagnostic ability of the parameters, a linear discriminant analysis with a leave-one-out cross-validation procedure was applied. The accuracies reached 83.9% and 65.9% to discriminate AD and MCI subjects from controls, respectively. Our findings suggest that MCI subjects exhibit an intermediate pattern of abnormalities between normal aging and AD. Furthermore, the proposed parameters provide a new description of brain dynamics in AD and MCI.

HERMES: Towards an Integrated Toolbox to Characterize Functional and Effective Brain Connectivity

The analysis of the interdependence between time series has become an important field of research in the last years, mainly as a result of advances in the characterization of dynamical systems from the signals they produce, the introduction of concepts such as generalized and phase synchronization and the application of information theory to time series analysis. In neurophysiology, different analytical tools stemming from these concepts have added to the ‘traditional’ set of linear methods, which includes the cross-correlation and the coherency function in the time and frequency domain, respectively, or more elaborated tools such as Granger Causality. This increase in the number of approaches to tackle the existence of functional (FC) or effective connectivity (EC) between two (or among many) neural networks, along with the mathematical complexity of the corresponding time series analysis tools, makes it desirable to arrange them into a unified-easy-to-use software package. The goal is to allow neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of these analysis methods from a single integrated toolbox. Here we present HERMES (http://hermes.ctb.upm.es), a toolbox for the Matlab® environment (The Mathworks, Inc), which is designed to study functional and effective brain connectivity from neurophysiological data such as multivariate EEG and/or MEG records. It includes also visualization tools and statistical methods to address the problem of multiple comparisons. We believe that this toolbox will be very helpful to all the researchers working in the emerging field of brain connectivity analysis.

HERMES: towards an integrated toolbox to characterize functional and effective brain connectivity

The analysis of the interdependence between time series has become an important field of research in the last years, mainly as a result of advances in the characterization of dynamical systems from the signals they produce, the introduction of concepts such as generalized and phase synchronization and the application of information theory to time series analysis. In neurophysiology, different analytical tools stemming from these concepts have added to the ?traditional? set of linear methods, which includes the cross-correlation and the coherency function in the time and frequency domain, respectively, or more elaborated tools such as Granger Causality. This increase in the number of approaches to tackle the existence of functional (FC) or effective connectivity (EC) between two (or among many) neural networks, along with the mathematical complexity of the corresponding time series analysis tools, makes it desirable to arrange them into a unified, easy-to-use software package. The goal is to allow neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of these analysis methods from a single integrated toolbox. Here we present HERMES (http://hermes.ctb.upm.es), a toolbox for the Matlab® environment (The Mathworks, Inc), which is designed to study functional and effective brain connectivity from neurophysiological data such as multivariate EEG and/or MEG records. It includes also visualization tools and statistical methods to address the problem of multiple comparisons. We believe that this toolbox will be very helpful to all the researchers working in the emerging field of brain connectivity analysis.

Security of plug-and-play QKD arrangements with finite resources

The security of a passive plug-and-play QKD arrangement in the case of finite (resources) key lengths is analysed. It is assumed that the eavesdropper has full access to the channel so an unknown and untrusted source is assumed. To take into account the security of the BB84 protocol under collective attacks within the framework of quantum adversaries, a full treatment provides the well-known equations for the secure key rate. A numerical simulation keeping a minimum number of initial parameters constant as the total error sought and the number of pulses is carried out. The remaining parameters are optimized to produce the maximum secure key rate. Two main strategies are addressed: with and without two-decoy-states including the optimization of signal to decoy relationship.

Entanglement distribution in optical networks

The ability to generate entangled photon pairs over a broad wavelength range opens the door to the simultaneous distribution of entanglement to multiple users in a network by using centralized sources and flexible wavelength-division multiplexing schemes. Here, we show the design of a metropolitan optical network consisting of tree-type access networks, whereby entangled photon pairs are distributed to any pair of users, independent of their location. The network is constructed employing commercial off-the-shelf components and uses the existing infrastructure, which allows for moderate deployment costs. We further develop a channel plan and a network-architecture design to provide a direct optical path between any pair of users; thus, allowing classical and one-way quantum communication, as well as entanglement distribution. This allows the simultaneous operation of multiple quantum information technologies. Finally, we present a more flexible backbone architecture that pushes away the load limitations of the original network design by extending its reach, number of users and capabilities.