Genuinely multipartite entangled states and orthogonal arrays

A pure quantum state of N subsystems with d levels each is called k-multipartite maximally entangled state, written k-uniform, if all its reductions to k qudits are maximally mixed. These states form a natural generalization of N-qudits GHZ states which belong to the class 1-uniform states. We establish a link between the combinatorial notion of orthogonal arrays and k-uniform states and prove the existence of several new classes of such states for N-qudit systems. In particular, known Hadamard matrices allow us to explicitly construct 2-uniform states for an arbitrary number of N>5 qubits. We show that finding a different class of 2-uniform states would imply the Hadamard conjecture, so the full classification of 2-uniform states seems to be currently out of reach. Additionally, single vectors of another class of 2-uniform states are one-to-one related to maximal sets of mutually unbiased bases. Furthermore, we establish links between existence of k-uniform states, classical and quantum error correction codes and provide a novel graph representation for such states.Comment: 24 pages, 7 figures. Comments are very welcome

Semiquantum secret sharing by using x-type states

In this paper, a semiquantum secret sharing (SQSS) protocol based on x-type states is proposed, which can accomplish the goal that only when two classical communicants cooperate together can they extract the shared secret key of a quantum communicant. Detailed security analysis turns out that this protocol can resist the participant attack and the outside attack. This protocol has some merits: (1) it only requires one kind of quantum entangled state as the initial quantum resource; (2) it doesn't employ quantum entanglement swapping or unitary operations; and (3) it needn't share private keys among different participants beforehand.Comment: 18 pages, 1 figure, 3 table

Quantum Computing and Communications

This book explains the concepts and basic mathematics of quantum computing and communication. Chapters cover such topics as quantum algorithms, photonic implementations of discrete-time quantum walks, how to build a quantum computer, and quantum key distribution and teleportation, among others

Mathematical surfaces models between art and reality

In this paper, I want to document the history of the mathematical surfaces models used for the didactics of pure and applied “High Mathematics” and as art pieces. These models were built between the second half of nineteenth century and the 1930s. I want here also to underline several important links that put in correspondence conception and construction of models with scholars, cultural institutes, specific views of research and didactical studies in mathematical sciences and with the world of the figurative arts furthermore. At the same time the singular beauty of form and colour which the models possessed, aroused the admiration of those entirely ignorant of their mathematical attraction

Continuous Variable Optimisation of Quantum Randomness and Probabilistic Linear Amplification

In the past decade, quantum communication protocols based on continuous variables (CV) has seen considerable development in both theoretical and experimental aspects. Nonetheless, challenges remain in both the practical security and the operating range for CV systems, before such systems may be used extensively. In this thesis, we present the optimisation of experimental parameters for secure randomness generation and propose a non-deterministic approach to enhance amplification of CV quantum state. The first part of this thesis examines the security of quantum devices: in particular, we investigate quantum random number generators (QRNG) and quantum key distribution (QKD) schemes. In a realistic scenario, the output of a quantum random number generator is inevitably tainted by classical technical noise, which potentially compromises the security of such a device. To safeguard against this, we propose and experimentally demonstrate an approach that produces side-information independent randomness. We present a method for maximising such randomness contained in a number sequence generated from a given quantum-to-classical-noise ratio. The detected photocurrent in our experiment is shown to have a real-time random-number generation rate of 14 (Mbit/s)/MHz. Next, we study the one-sided device-independent (1sDI) quantum key distribution scheme in the context of continuous variables. By exploiting recently proven entropic uncertainty relations, one may bound the information leaked to an eavesdropper. We use such a bound to further derive the secret key rate, that depends only upon the conditional Shannon entropies accessible to Alice and Bob, the two honest communicating parties. We identify and experimentally demonstrate such a protocol, using only coherent states as the resource. We measure the correlations necessary for 1sDI key distribution up to an applied loss equivalent to 3.5 km of fibre transmission. The second part of this thesis concerns the improvement in the transmission of a quantum state. We study two approximate implementations of a probabilistic noiseless linear amplifier (NLA): a physical implementation that truncates the working space of the NLA or a measurement-based implementation that realises the truncation by a bounded postselection filter. We do this by conducting a full analysis on the measurement-based NLA (MB-NLA), making explicit the relationship between its various operating parameters, such as amplification gain and the cut-off of operating domain. We compare it with its physical counterpart in terms of the Husimi Q-distribution and their probability of success. We took our investigations further by combining a probabilistic NLA with an ideal deterministic linear amplifier (DLA). In particular, we show that when NLA gain is strictly lesser than the DLA gain, this combination can be realised by integrating an MB-NLA in an optical DLA setup. This results in a hybrid device which we refer to as the heralded hybrid quantum amplifier. A quantum cloning machine based on this hybrid amplifier is constructed through an amplify-then-split method. We perform probabilistic cloning of arbitrary coherent states, and demonstrate the production of up to five clones, with the fidelity of each clone clearly exceeding the corresponding no-cloning limit

Measurements, Models, Systems and Design

531 s.

Efficient generation of photonic entanglement and multiparty quantum communication

Entangled photons are at the heart of experimental quantum physics. They were used for the first fundamental tests of quantum theory, and became a basic building block for many novel quantum protocols, such as quantum cryptography, dense coding or teleportation. Therefore, the efficient generation of entangled photons, as well as their distribution and accurate analysis are of paramount importance, particularly with regard to the practicability of many applications of quantum communication. This thesis deals largely with the problem of efficient generation of photonic entanglement with the principal aim of developing a bright source of polarization-entangled photon pairs, which meets the requirements for reliable and economic operation of quantum communication prototypes and demonstrators. Our approach uses a correlated photon-pair emission in nonlinear process of spontaneous parametric down-conversion pumped by light coming from a compact and cheap blue laser diode. Two alternative source configurations are examined within the thesis. The first makes use of a well established concept of degenerate non-collinear emission from a single type-II nonlinear crystal and the second relies on a novel method where the emissions from two adjacent type-I phase-matched nonlinear crystals operated in collinear non-degenerate regime are coherently overlapped. The latter approach showed to be more effective, yielding a total detected rate of almost 10^6 pairs/s at >98 % quantum interference visibility of polarization correlations. This performance, together with the almost free of alignment operation of the system, suggest that it is an especially promising candidate for many future practical applications, including quantum cryptography, detector calibration or use in undergraduate lab courses. The second issue addressed within the thesis is the simplification and practical implementation of quantum-assisted solutions to multiparty communication tasks. While the recent rapid progress in the development of bright entangled photon-pair sources has been followed with ample experimental reports on two-party quantum communication tasks, the practical implementations of tasks for more than two parties have been held back, so far. This is mainly due to the requirement of multiparty entangled states, which are very difficult to be produced with current methods and moreover suffer from a high noise. We show that entanglement is not the only non-classical resource endowing the quantum multiparty information processing its power. Instead, only the sequential communication and transformation of a single qubit can be sufficient to accomplish certain tasks. This we prove for two distinct communication tasks, secret sharing and communication complexity. Whereas the goal of the first is to split a cryptographic key among several parties in a way that its reconstruction requires their collaboration, the latter aims at reducing the amount of communication during distributed computational tasks. Importantly, our qubit-assisted solutions to the problems are feasible with state-of-the-art technology. This we clearly demonstrate in the laboratory implementation for 6 and 5 parties, respectively, which is to the best of our knowledge the highest number of actively performing parties in a quantum protocol ever implemented. Thus, by successfully solving and implementing a cryptographic task as well as a task originating in computer science, we clearly illustrate the potential to introduce multiparty communication problems into real life.Verschränkte Photonen sind von zentralem Interesse im Bereich experimenteller Quantenphysik. Sie wurden für die ersten fundamentalen Tests der Quantentheorie verwendet und bilden die Grundlage bei der Realisierung vieler neuer Kommunikationsprotokolle die auf quantenmechanischen Effekten basieren, wie zum Beispiel Quantenkryptographie, "dense coding" oder Teleportation. Die effiziente Erzeugung verschränkter Photonen sowie deren genaue Analyse ist folglich von großer Bedeutung, insbesondere im Hinblick auf die Umsetzbarkeit der vielen Quantenkommunikationsanwendungen. Die vorliegende Arbeit behandelt im Wesentlichen das Problem der effizienten Erzeugung von Photon Verschränkung. Das Hauptaugenmerk liegt dabei auf der Entwicklung einer Quelle verschränkter Photonen, die den Anforderungen für einen zuverlässigen und wirtschaftlichen Betrieb in Beispielanwendungen der Quantenkommunikation genügt. Unser Ansatz verwendet die Emission korrelierter Photonen Paare im Prozess der spontanen parametrischen Fluoreszenz. Der Prozess wird mit Licht einer handlichen und billigen blauen Laserdiode gepumpt. Es werden zwei alternative Aufbauten für die Quelle betrachtet. Der erste verwendet das altbewährte Konzept der entarteten nicht-kollinearen Emission in einem einzelnen nichtlinearen Kristall vom Typ II. Der zweite Ansatz basiert auf einer neuen Methode in der die Emission zweier aneinaderliegender, phasenangepasster Kristalle vom Typ I kohärent überlagert wird. Die Phasenanpassung erfolgt dabei im kollinearen nicht-entarteten Zustand. Mit einer Rate von 10^6 Paaren in der Sekunde bei einem Interferenzkontrast der Polarisationskorrelationen von >98 % erwies sich die neue Methode als wesentlich effizienter. Diese Leistungsfähigkeit, in Verbindung mit einem nahezu justagefreien Betrieb, lässt dieses System vielversprechend für zukünftige praktische Anwendungen, wie Quantenkryptographie, Detektorkalibrierung oder Praktikumsversuche für Studenten erscheinen. Ein weiteres Thema das im Rahmen dieser Arbeit behandelt wird ist die Vereinfachung und Implementierung kommunikationstheoretischer Problemlösungen unter Zuhilfenahme quantenmechanischer Effekte. Während der rasante Fortschritt der letzten Jahre bei der Entwicklung von Quellen zur Erzeugung verschränkter Photonenpaare zu einer großen Anzahl von Veröffentlichungen auf dem Gebiet der Zwei-Parteien-Quantenkommunikation geführt hat, hielt sich die Zahl der Implementierungen von Protokollen mit mehr als zwei Parteien in Grenzen. Dies liegt hauptsächlich daran, dass die benötigten Mehr-Teilchen verschränkten Zustände mit dem heutigen Stand der Technik schwer zu produzieren sind und darüber hinaus hohes Rauschen aufweisen. Wir zeigen, dass Verschränkung nicht die einzige Ressource ist, die Mehrparteien-Quanten-Informationsverarbeitung ihre Stärke verleiht. Im Gegenteil, die sequentielle Kommunikation und Transformation eines einzelnen Qubits kann bereits ausreichend für die Lösung bestimmter Probleme sein. Dies zeigen wir anhand zweier verschiedener informationstheoretischer Problemstellungen, dem "secret sharing" und der Kommunikationskomplexität. Die erste befasst sich mit der Aufteilung eines kryptographischen Schlüssels auf mehrere Parteien in einer Weise, die für dessen Rekonstruktion die Zusammenarbeit aller Parteien erfordert. Die zweite zielt auf die Reduzierung der Kommunikation beim Lösen distributiver Berechnungen ab. Bemerkenswerterweise ist das hier verwendete qubit-basierte Lösungsverfahren mit dem heutigen Stand der Technik umsetzbar, was wir durch dessen Realisierung im Labor für 6 bzw. 5 Personen zeigen. Nach unserem Wissen ist dies die höchste Anzahl an aktiv agierenden Teilnehmern in einem Quantenkommunikationsprotokoll die je implementiert wurde. Die erfolgreiche Lösung und Implementierung von Problemstellungen aus den Bereichen der Kryptographie und der Informatik bringt somit Mehrparteien Quantenkommunikation einen Schritt näher an kommerzielle Anwendungen heran