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.

O canal de distribuição para produtos cosméticos em Porto Alegre : uma análise com foco nos salões de beleza

As empresas estão participando de um mercado cada vez mais competitivo. Esta disputa acirrada das empresas pelos clientes tem propiciado canais alternativos de distribuição dos produtos aos diferentes segmentos de mercado. Os canais de distribuição estão adquirindo uma importância cada vez maior aos olhos dos fabricantes e dos clientes, principalmente na questão de serviços. De acordo com Ballou (2001, p.44), “o serviço ao cliente, inclui disponibilidade de estoques, rapidez na entrega, rapidez e acuracidade no preenchimento de pedidos”. A esses serviços pode ser somada uma gama variada de outros serviços a serem prestados pelos participantes do canal de distribuição ou pelos fabricantes. A empresa Ravel Produtos Cosméticos e Dermatológicos será a principal usuária dos resultados obtidos com este estudo, pois é fabricante de produtos cosméticos e tem seu foco de atuação principal na cidade de Porto Alegre. O objetivo deste trabalho foi analisar o canal de distribuição para produtos cosméticos destinados a consumidores de alta renda no mercado de Porto Alegre, procurando identificar os aspectos de serviços demandados, produtos utilizados e mix de produtos comercializados pelo canal de distribuição: salões de beleza. O estudo foi realizado através de pesquisa qualitativa, com entrevistas individuais junto aos proprietários dos salões, ou junto às pessoas que decidem o mix de produtos a ser utilizado ou comercializado pelos salões. O mix de produtos comercializados pelos salões de beleza em Porto Alegre conforme a pesquisa realizada, é o seguinte: xampus, cremes, máscaras, hidratantes, fluidos e géis. Entre as respostas das entrevistas, foram encontrados os seguintes serviços demandados pelos salões de beleza: amostras de produtos, entregas rápidas, frete cif, suporte técnico do fabricante, prazos elásticos de pagamento e exclusividade como canal de distribuição para as linhas que comercializa.

A New Cryptographic Scheme for Securing Dynamic Conferences in Data Networks

Dynamic conferencing refers to a scenario wherein any subset of users in a universe of users form a conference for sharing confidential information among themselves. The key distribution (KD) problem in dynamic conferencing is to compute a shared secret key for such a dynamically formed conference. In literature, the KD schemes for dynamic conferencing either are computationally unscalable or require communication among users, which is undesirable. The extended symmetric polynomial based dynamic conferencing scheme (ESPDCS) is one such KD scheme which has a high computational complexity that is universe size dependent. In this paper we present an enhancement to the ESPDCS scheme to develop a KD scheme called universe-independent SPDCS (UI-SPDCS) such that its complexity is independent of the universe size. However, the UI-SPDCS scheme does not scale with the conference size. We propose a relatively scalable KD scheme termed as DH-SPDCS that uses the UI-SPDCS scheme and the tree-based group Diffie- Hellman (TGDH) key exchange protocol. The proposed DH-SPDCS scheme provides a configurable trade-off between computation and communication complexity of the scheme.

QUANTUM CORRELATIONS OF LIGHTS IN MACROSCOPIC ENVIRONMENTS

This dissertation presents a detailed study in exploring quantum correlations of lights in macroscopic environments. We have explored quantum correlations of single photons, weak coherent states, and polarization-correlated/polarization-entangled photons in macroscopic environments. These included macroscopic mirrors, macroscopic photon number, spatially separated observers, noisy photons source and propagation medium with loss or disturbances. We proposed a measurement scheme for observing quantum correlations and entanglement in the spatial properties of two macroscopic mirrors using single photons spatial compass state. We explored the phase space distribution features of spatial compass states, such as chessboard pattern by using the Wigner function. The displacement and tilt correlations of the two mirrors were manifested through the propensities of the compass states. This technique can be used to extract Einstein-Podolsky-Rosen correlations (EPR) of the two mirrors. We then formulated the discrete-like property of the propensity Pb(m,n), which can be used to explore environmental perturbed quantum jumps of the EPR correlations in phase space. With single photons spatial compass state, the variances in position and momentum are much smaller than standard quantum limit when using a Gaussian TEM00 beam. We observed intrinsic quantum correlations of weak coherent states between two parties through balanced homodyne detection. Our scheme can be used as a supplement to decoy-state BB84 protocol and differential phase-shift QKD protocol. We prepared four types of bipartite correlations ±cos2(θ12) that shared between two parties. We also demonstrated bits correlations between two parties separated by 10 km optical fiber. The bits information will be protected by the large quantum phase fluctuation of weak coherent states, adding another physical layer of security to these protocols for quantum key distribution. Using 10 m of highly nonlinear fiber (HNLF) at 77 K, we observed coincidence to accidental-coincidence ratio of 130±5 for correlated photon-pair and Two-Photon Interference visibility >98% entangled photon-pair. We also verified the non-local behavior of polarization-entangled photon pair by violating Clauser-Horne-Shimony-Holt Bell’s inequality by more than 12 standard deviations. With the HNLF at 300 K (77 K), photon-pair production rate about factor 3(2) higher than a 300 m dispersion-shifted fiber is observed. Then, we studied quantum correlation and interference of photon-pairs; with one photon of the photon-air experiencing multiple scattering in a random medium. We observed that depolarization noise photon in multiple scattering degrading the purity of photon-pair, and the existence of Raman noise photon in a photon-pair source will contribute to the depolarization affect. We found that quantum correlation of polarization-entangled photon-pair is better preserved than polarization-correlated photon-pair as one photon of the photon-pair scattered through a random medium. Our findings showed that high purity polarization-entangled photon-pair is better candidate for long distance quantum key distribution.

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.

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.

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.

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.

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.

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.

Networks based on QKD and weakly trusted repeaters

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 secret-key distribution that relies only on the fundamental principles of quantum physics. Point-to-point QKD devices 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 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.

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.

Dynamical creation of entanglement by homodyne-mediated feedback

For two two-level atoms coupled to a single Bosonic mode that is driven and heavily damped, the steady state can be entangled by resonantly driving the system [S. Schneider and G. J. Milburn, Phys. Rev. A 65, 042107 (2002)]. We present a scheme to significantly increase the steady-state entanglement by using homodyne-mediated feedback, in which the Bosonic mode is that of an electromagnetic cavity, the output of which is measured and the resulting homodyne photocurrent is used to modulate the field driving the qubits. Such feedback can increase the nonlinear response to both the decoherence process of the two-qubit system and the coherent evolution of individual qubits. We present the properties of the entangled states using the SO(3) Q function.