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.

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.

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.

Information reconciliation for Quantum Key Distribution

Secret-key agreement, a well-known problem in cryptography, allows two parties holding correlated sequences to agree on a secret key communicating over a public channel. It is usually divided into three different procedures: advantage distillation, information reconciliation and privacy amplification. The efficiency of each one of these procedures is needed if a positive key rate is to be attained from the legitimate parties? correlated sequences. Quantum key distribution (QKD) allows the two parties to obtain correlated sequences, provided that they have access to an authenticated channel. The new generation of QKD devices is able to work at higher speeds and in noisier or more absorbing environments. This exposes the weaknesses of current information reconciliation protocols, a key component to their performance. Here we present a new protocol based in low-density parity-check (LDPC) codes that presents the advantages of low interactivity, rate adaptability and high efficiency,characteristics that make it highly suitable for next generation QKD devices.

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.

Nanotechnology for more efficient photovoltaics: the quantum dot intermediate band solar cell

The intermediate band solar cell [1] has been proposed as a concept able to substantially enhance the efficiency limit of an ordinary single junction solar cell. If a band permitted for electrons is inserted within the forbidden band of a semiconductor then a novel path for photo generation is open: electron hole pairs may be formed by the successive absorption of two sub band gap photons using the intermediate band (IB) as a stepping stone. While the increase of the photovoltaic (PV) current is not a big achievement —it suffices to reduce the band gap— the achievement of this extra current at high voltage is the key of the IB concept. In ordinary cells the voltage is limited by the band gap so that reducing it would also reduce the band gap. In the intermediate band solar cell the high voltage is produced when the IB is permitted to have a Quasi Fermi Level (QFL) different from those of the Conduction Band (CB) and the Valence Band (VB). For it the cell must be properly isolated from the external contacts, which is achieved by putting the IB material between two n- and p-type ordinary semiconductors [2]. Efficiency thermodynamic limit of 63% is obtained for the IB solar cell1 vs. the 40% obtained [3] for ordinary single junction solar cells. Detailed information about the IB solar cells can be found elsewhere [4].

Secure optical networks based on quantum key distribution and weakly trusted repeaters

Abstract—In this paper we explore how recent technologies can improve the security of optical networks. In particular, we study how to use quantum key distribution(QKD) in common optical network infrastructures and propose a method to overcome its distance limitations. QKD is the first technology offering information theoretic secretkey distribution that relies only on the fundamental principles of quantum physics. Point-to-point QKDdevices have reached a mature industrial state; however, these devices are severely limited in distance, since signals at the quantum level (e.g., single photons) are highly affected by the losses in the communication channel and intermediate devices. To overcome this limitation, intermediate nodes (i.e., repeaters) are used. Both quantum-regime and trusted, classical repeaters have been proposed in the QKD literature, but only the latter can be implemented in practice. As a novelty, we propose here a new QKD network model based on the use of not fully trusted intermediate nodes, referred to as weakly trusted repeaters. This approach forces the attacker to simultaneously break several paths to get access to the exchanged key, thus improving significantly the security of the network. We formalize the model using network codes and provide real scenarios that allow users to exchange secure keys over metropolitan optical networks using only passive components. Moreover, the theoretical framework allows one to extend these scenarios not only to accommodate more complex trust constraints, but also to consider robustness and resiliency constraints on the network.

An information reconciliation protocol for secret-key agreement with small leakage

We report on a variant of the so-called Cascade protocol that is well-known for its usage as information reconciliation protocol in quantum cryptography. A theoretical analysis of the optimal size of the parity check blocks is provided. We obtain a very small leakage which is for block sizes of 2^16 typically only 2.5% above the Shannon limit, and notably, this holds for a QBER between 1% and 50%. For a QBER between 1% and 6% the leakage is only 2% above the Shannon limit. As comparison, the leakage of the original Cascade algorithm is 20% (40%) above the Shannon limit for a QBER of 10% (35%).

Rate-Adaptive LDPC-based key reconciliation for high performance quantum key distribution

The postprocessing or secret-key distillation process in quantum key distribution (QKD) mainly involves two well-known procedures: information reconciliation and privacy amplification. Information or key reconciliation has been customarily studied in terms of efficiency. During this, some information needs to be disclosed for reconciling discrepancies in the exchanged keys. The leakage of information is lower bounded by a theoretical limit, and is usually parameterized by the reconciliation efficiency (or inefficiency), i.e. the ratio of additional information disclosed over the Shannon limit. Most techniques for reconciling errors in QKD try to optimize this parameter. For instance, the well-known Cascade (probably the most widely used procedure for reconciling errors in QKD) was recently shown to have an average efficiency of 1.05 at the cost of a high interactivity (number of exchanged messages). Modern coding techniques, such as rate-adaptive low-density parity-check (LDPC) codes were also shown to achieve similar efficiency values exchanging only one message, or even better values with few interactivity and shorter block-length codes.

Efficient information reconciliation for Continuous-Variable QKD using Non-Binary Low-Density Parity-Check Codes

We present here an information reconciliation method and demonstrate for the first time that it can achieve efficiencies close to 0.98. This method is based on the belief propagation decoding of non-binary LDPC codes over finite (Galois) fields. In particular, for convenience and faster decoding we only consider power-of-two Galois fields.

Implications of low breakdown voltage of component subcells on external quantum efficiency measurements of multijunction solar cells

The electrical and optical coupling between subcells in a multijunction solar cell affects its external quantum efficiency (EQE) measurement. In this study, we show how a low breakdown voltage of a component subcell impacts the EQE determination of a multijunction solar cell and demands the use of a finely adjusted external voltage bias. The optimum voltage bias for the EQE measurement of a Ge subcell in two different GaInP/GaInAs/Ge triple-junction solar cells is determined both by sweeping the external voltage bias and by tracing the I–V curve under the same light bias conditions applied during the EQE measurement. It is shown that the I–V curve gives rapid and valuable information about the adequate light and voltage bias needed, and also helps to detect problems associated with non-ideal I–V curves that might affect the EQE measurement. The results also show that, if a non-optimum voltage bias is applied, a measurement artifact can result. Only when the problems associated with a non-ideal I–V curve and/or a low breakdown voltage have been discarded, the measurement artifacts, if any, can be attributed to other effects such as luminescent coupling between subcells.