Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

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.

Proposal for a Wavelength Multiplexed Quantum Metropolitan Area Network

Quantum Key Distribution (QKD) is maturing quickly. However, the current approaches to its network use require conditions that make it an expensive technology. All the QKD networks deployed to date are designed as a collection of dedicated point-to-point links that use the trusted repeater paradigm. Instead, we propose a novel network model in which QKD systems use simultaneously quantum and conventional signals that are wavelength multiplexed over a common communication infrastructure. Signals are transmitted end-to-end within a metropolitan area using optical components. The model resembles a commercial telecom network and takes advantage of existing components, thus allowing for a cost-effective and reliable deployment.

Quantum metropolitan optical network based on wavelength division multiplexing

Quantum Key Distribution (QKD) is maturing quickly. However, the current approaches to its application in optical networks make it an expensive technology. QKD networks deployed to date are designed as a collection of point-to-point, dedicated QKD links where non-neighboring nodes communicate using the trusted repeater paradigm. We propose a novel optical network model in which QKD systems share the communication infrastructure by wavelength multiplexing their quantum and classical signals. The routing is done using optical components within a metropolitan area which allows for a dynamically any-to-any communication scheme. Moreover, it resembles a commercial telecom network, takes advantage of existing infrastructure and utilizes commercial components, allowing for an easy, cost-effective and reliable deployment.

Quantum cryptography without switching

We propose a new coherent state quantum key distribution protocol that eliminates the need to randomly switch between measurement bases. This protocol provides significantly higher secret key rates with increased bandwidths than previous schemes that only make single quadrature measurements. It also offers the further advantage of simplicity compared to all previous protocols which, to date, have relied on switching.

Efficient entanglement distillation without quantum memory

Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution.

Polarization effects in fiber-optic communication systems

In this thesis we perform a detailed analysis of the state of polarization (SOP) of light scattering process using a concatenation of ber-coil based polarization controllers (PCs). We propose a polarization-mode dispersion (PMD) emulator, built through the concatenation of bercoil based PCs and polarization-maintaining bers (PMFs), capable of generate accurate rst- and second-order PMD statistics. We analyze the co-propagation of two optical waves inside a highbirefringence ber. The evolution along the ber of the relative SOP between the two signals is modeled by the de nition of the degree of co-polarization parameter. We validate the model for the degree of co-polarization experimentally, exploring the polarization dependence of the four-wave mixing e ect into a ber with high birefringence. We also study the interaction between signal and noise mediated by Kerr e ect in optical bers. A model accurately describing ampli ed spontaneous emission noise in systems with distributed Raman gain is derived. We show that the noise statistics depends on the propagation distance and on the signal power, and that for distances longer than 120 km and signal powers higher than 6 mW it deviates signi catively from the Gaussian distribution. We explore the all-optical polarization control process based on the stimulated Raman scattering e ect. Mapping parameters like the degree of polarization (DOP), we show that the preferred ampli cation of one particular polarization component of the signal allows a polarization pulling over a wavelength range of 60 nm. The e ciency of the process is higher close to the maximum Raman gain wavelength, where the DOP is roughly constant for a wavelength range of 15 nm. Finally, we study the polarization control in quantum key distribution (QKD) systems with polarization encoding. A model for the quantum bit error rate estimation in QKD systems with time-division multiplexing and wavelength-division multiplexing based polarization control schemes is derived.

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.

Crypto topics and applications II

In this chapter we continue the exposition of crypto topics that was begun in the previous chapter. This chapter covers secret sharing, threshold cryptography, signature schemes, and finally quantum key distribution and quantum cryptography. As in the previous chapter, we have focused only on the essentials of each topic. We have selected in the bibliography a list of representative items, which can be consulted for further details. First we give a synopsis of the topics that are discussed in this chapter. Secret sharing is concerned with the problem of how to distribute a secret among a group of participating individuals, or entities, so that only predesignated collections of individuals are able to recreate the secret by collectively combining the parts of the secret that were allocated to them. There are numerous applications of secret-sharing schemes in practice. One example of secret sharing occurs in banking. For instance, the combination to a vault may be distributed in such a way that only specified collections of employees can open the vault by pooling their portions of the combination. In this way the authority to initiate an action, e.g., the opening of a bank vault, is divided for the purposes of providing security and for added functionality, such as auditing, if required. Threshold cryptography is a relatively recently studied area of cryptography. It deals with situations where the authority to initiate or perform cryptographic operations is distributed among a group of individuals. Many of the standard operations of single-user cryptography have counterparts in threshold cryptography. Signature schemes deal with the problem of generating and verifying electronic) signatures for documents.Asubclass of signature schemes is concerned with the shared-generation and the sharedverification of signatures, where a collaborating group of individuals are required to perform these actions. A new paradigm of security has recently been introduced into cryptography with the emergence of the ideas of quantum key distribution and quantum cryptography. While classical cryptography employs various mathematical techniques to restrict eavesdroppers from learning the contents of encrypted messages, in quantum cryptography the information is protected by the laws of physics.

Control circuits for avalanche photodiodes

Avalanche Photodiodes (APDs) have been used in a wide range of low light sensing applications such as DNA sequencing, quantum key distribution, LIDAR and medical imaging. To operate the APDs, control circuits are required to achieve the desired performance characteristics. This thesis presents the work on development of three control circuits including a bias circuit, an active quench and reset circuit and a gain control circuit all of which are used for control and performance enhancement of the APDs. The bias circuit designed is used to bias planar APDs for operation in both linear and Geiger modes. The circuit is based on a dual charge pumps configuration and operates from a 5 V supply. It is capable of providing milliamp load currents for shallow-junction planar APDs that operate up to 40 V. With novel voltage regulators, the bias voltage provided by the circuit can be accurately controlled and easily adjusted by the end user. The circuit is highly integrable and provides an attractive solution for applications requiring a compact integrated APD device. The active quench and reset circuit is designed for APDs that operate in Geiger-mode and are required for photon counting. The circuit enables linear changes in the hold-off time of the Geiger-mode APD (GM-APD) from several nanoseconds to microseconds with a stable setting step of 6.5 ns. This facilitates setting the optimal `afterpulse-free' hold-off time for any GM-APD via user-controlled digital inputs. In addition this circuit doesn’t require an additional monostable or pulse generator to reset the detector, thus simplifying the circuit. Compared to existing solutions, this circuit provides more accurate and simpler control of the hold-off time while maintaining a comparable maximum count-rate of 35.2 Mcounts/s. The third circuit designed is a gain control circuit. This circuit is based on the idea of using two matched APDs to set and stabilize the gain. The circuit can provide high bias voltage for operating the planar APD, precisely set the APD’s gain (with the errors of less than 3%) and compensate for the changes in the temperature to maintain a more stable gain. The circuit operates without the need for external temperature sensing and control electronics thus lowering the system cost and complexity. It also provides a simpler and more compact solution compared to previous designs. The three circuits designed in this project were developed independently of each other and are used for improving different performance characteristics of the APD. Further research on the combination of the three circuits will produce a more compact APD-based solution for a wide range of applications.

QKD in standard optical telecommunications networks

To perform Quantum Key Distribution, the mastering of the extremely weak signals carried by the quantum channel is required. Transporting these signals without disturbance is customarily done by isolating the quantum channel from any noise sources using a dedicated physical channel. However, to really profit from this technology, a full integration with conventional network technologies would be highly desirable. Trying to use single photon signals with others that carry an average power many orders of magnitude bigger while sharing as much infrastructure with a conventional network as possible brings obvious problems. The purpose of the present paper is to report our efforts in researching the limits of the integration of QKD in modern optical networks scenarios. We have built a full metropolitan area network testbed comprising a backbone and an access network. The emphasis is put in using as much as possible the same industrial grade technology that is actually used in already installed networks, in order to understand the throughput, limits and cost of deploying QKD in a real network.

On QKD industrialization

During the 25 years of existence of the first protocol for Quantum Key Distribution, much has been said and expected of what came to be termed as Quantum Cryptography. After all this time, much progress has been done but also the reality check and analysis that naturally comes with maturity is underway. A new panorama is emerging, and the way in which the challenges imposed by market requirements are tackled will determine the fate of Quantum Cryptography. The present paper attempts to frame a reasonable view on the issues of the security and market requirements that QKD should achieve to become a marketable technology.

Analysis of a rate-adaptive reconciliation protocol and the effect of leakage on the secret key rate

Quantum key distribution performs the trick of growing a secret key in two distant places connected by a quantum channel. The main reason is so that the legitimate users can bound the information gathered by the eavesdropper. In practical systems, whether because of finite resources or external conditions, the quantum channel is subject to fluctuations. A rate-adaptive information reconciliation protocol, which adapts to the changes in the communication channel, is then required to minimize the leakage of information in the classical postprocessing. We consider here the leakage of a rate-adaptive information reconciliation protocol. The length of the exchanged messages is larger than that of an optimal protocol; however, we prove that the min-entropy reduction is limited. The simulation results, both in the asymptotic and in the finite-length regime, show that this protocol allows to increase the amount of a distillable secret key.

Towards an Optimal Implementation of 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.