In this dissertation I develop a Monte-Carlo sampling approach to redress the enormous computational time required to calculate two-photon visibility for multiple-entanglementswapping-based long-distance quantum communication. I employ our theory to study both the realistic setting involving dark counts, multi-photon events and loss, and I also study the semi-idealistic case of perfect synchronized single-photon sources; this semi-idealistic case is used to verify my sampling method. My new sampling method enables successful, reliable calculation of visibility for up to six consecutive entanglementswapping stations. Although six entanglement-swapping stations lead to extremely low rates in the real-world setting, my sampling method for solving long-distance quantum communication rates and visibility serves as a valuable tool for modeling future viable quantum communication strategies incorporating promising technology such as optical quantum memory. past twenty-three years, and my dear friends, without whom my life can never be that wonderful. Finally, I want to thank her, who is the reason why I never give up on this project.
In this dissertation I develop a Monte-Carlo sampling approach to redress the enormous computational time required to calculate two-photon visibility for multiple-entanglementswapping-based long-distance quantum communication. I employ our theory to study both the realistic setting involving dark counts, multi-photon events and loss, and I also study the semi-idealistic case of perfect synchronized single-photon sources; this semi-idealistic case is used to verify my sampling method. My new sampling method enables successful, reliable calculation of visibility for up to six consecutive entanglementswapping stations. Although six entanglement-swapping stations lead to extremely low rates in the real-world setting, my sampling method for solving long-distance quantum communication rates and visibility serves as a valuable tool for modeling future viable quantum communication strategies incorporating promising technology such as optical quantum memory. past twenty-three years, and my dear friends, without whom my life can never be that wonderful. Finally, I want to thank her, who is the reason why I never give up on this project.
We develop a theory and accompanying mathematical model for quantum communication via any number of intermediate entanglement-swapping operations and solve numerically for up to three intermediate entanglement-swapping operations. Our model yields two-photon interference visibilities postselected on photon counts at the intermediate entanglement-swapping stations. Realistic experimental conditions are accommodated through the parametric down-conversion rate, photon-counter efficiencies and dark-count rates, and instrument and transmission losses. We calculate achievable quantum communication distances such that two-photon interference visibility exceeds the Bell-inequality threshold.
We construct a theory for long-distance quantum communication based on sharing entanglement through a linear chain of N elementary swapping segments of length L=Nl where l is the length of each elementary swap setup. Entanglement swapping is achieved by linear optics, photon counting, and postselection, and we include effects due to multiphoton sources, transmission loss, and detector inefficiencies and dark counts. Specifically we calculate the resultant four-mode state shared by the two parties at the two ends of the chain, and we derive the two-photon coincidence rate expected for this state and thereby the visibility of this long-range-entangled state. The expression is a nested sum with each sum extending from zero to infinite photons, and we solve the case N=2 exactly for the ideal case (zero dark counts, unit-efficiency detectors, and no transmission loss) and numerically for N=2 in the nonideal case with truncation at nmax=3 photons in each mode. For the general case, we show that the computational complexity for the numerical solution is nmax12N.
Long-distance transfer of quantum information is an essential ability for many applications of quantum science. A natural choice to distribute quantum information is to encode it into photons and transfer it through optical fibers. However, due to the unavoidable transmission losses present in every communication channel, the distances for efficient quantum communication via direct-state transfer are limited to a few hundred kilometers. To overcome this limitation, the use of quantum repeaters has been suggested. A quantum repeater protocol aims to establish entanglement (i.e., quantum correlation) between remote nodes by first generating entanglement over shorter distance pieces, storing it in quantum memories, and finally extending it to the whole distance using entanglement swapping. The main goal of this thesis is to design quantum repeater architectures using single solid-state quantum emitters and to develop the two-qubit gates required for performing entanglement swapping. We first explain the basic ideas of quantum repeaters and introduce potential material candidates, single erbium (168Er) and europium (151Eu) ions doped yttrium orthosilicate photonic crystals. Next, we propose a quantum repeater scheme combing erbium and europium ions to generate and distribute entanglement over long distances. We study the entanglement generation rate of the protocol and compare it with the rate of a well-known ensemble-based quantum repeater. Then, using cavity assisted interactions, we propose three different schemes to perform high fidelity two-qubit gates between single quantum systems. We quantify their expected performance in detail by taking into account many realistic imperfections and compare their strengths and weaknesses. The ability to perform local two-qubits gates is especially crucial in terms of distributing entanglement. Finally, based on our gained knowledge through these projects, we propose our second quantum repeater architecture based on erbium (167Er) ions, which outperforms the first scheme. We study two possibilities for distributing entanglement and calculate the overall fidelity as well as the distribution rate of the protocol.
This thesis examines the integration of two disparate technologies in order to perform experiments in single photon quantum optics with low loss. Many technologies and experiments in quantum optics, communication, or computing require a certain fraction of the photons involved to be received at the end of the experiment, and in many cases the required efficiency has not yet been reached. This includes the famous Einstein, Podolsky, and Rosen gedanken-experiment, now implemented in the laboratory, demonstrating the existence of entanglement to unconvinced observers. Also included is the nonlocality test of John Bell, as well as technological problems such as device-independent quantum key distribution. In this thesis I perform these experiments in the high-efficiency regime. This programme requires the integration of two lines of research: improving sources of single photons, and improving detectors thereof. Until recently detector research was focussed on development, with improvements being sought for their own sake, working towards the ultimate goal of perfect photon detection. Recent years have seen these devices move into quantum photonics laboratories, allowing for previously impossible experiments to be undertaken. In this thesis, I combine high-efficiency, number-resolving, detectors with a high-efficiency entangled photon pair source, based on another line of research going back decades: the use of spontaneous parametric down-conversion to create single-photon-like modes of light, and the entanglement of the output modes in a useful way. For small demonstrations, such as the experiments mentioned above, this can emulate a single photon with enough fidelity, and low enough loss, to successfully perform the procedure. Here I push both of these technologies, and the problems of combining them, as far as I can, and solve the problems inherent with any marriage of disparate devices. I also examine the relative performance of two different steering inequalities, one linear and one quadratic, in the presence of noise, analysing my experimental data with each of them. I perform a detection- loophole free demonstration of EPR steering, violating the local bound by 200s, setting a then world record for efficiency at 62.5%.
This Thesis contributes to the theory of entanglement distribution in quantum networks, analyzing the generation of long-distance entanglement in particular.We consider that neighboring stations share one partially entangled pair of qubits, which emphasizes the difficulty of creating remote entanglement in realistic settings.The task is then to design local quantum operations at the stations, such that the entanglement present in the links of the whole network gets concentrated between few parties only, regardless of their spatial arrangement.First, we study quantum networks with a two-dimensional lattice structure, where quantum connections between the stations (nodes) are described by non-maximally entangled pure states (links).We show that the generation of a perfectly entangled pair of qubits over an arbitrarily long distance is possible if the initial entanglement of the links is larger than a threshold.This critical value highly depends on the geometry of the lattice, in particular on the connectivity of the nodes, and is related to a classical percolation problem.We then develop a genuine quantum strategy based on multipartite entanglement, improving both the threshold and the success probability of the generation of long-distance entanglement.Second, we consider a mixed-state definition of the connections of the quantum networks.This formalism is well-adapted for a more realistic description of systems in which noise (random errors) inevitably occurs.New techniques are required to create remote entanglement in this setting, and we show how to locally extract and globally process some error syndromes in order to create useful long-distance quantum correlations.Finally, we turn to networks that have a complex topology, which is the case for most real-world communication networks such as the Internet for instance.Besides many other characteristics, these systems have in common the small-world feature, stating that any two nodes are separated by a few links only.Based on the theory of random graphs, we propose a model of quantum complex networks, which exhibit some totally unexpected properties compared to their classical counterparts.5.1 Propagation of a large GHZ state through the lattice . . .5.2 Bit-flip error correction . . . . . . . . . . . . .
We develop a theory for long-distance quantum key distribution based on concatenated entanglement swapping using parametric down-conversion sources and show the numerical results of our model. The model incorporates practical resources including multipair sources, inefficient detectors with dark counts, and lossy channels. We calculate the maximum secret key-generation rate for up to three entanglement swapping stations by optimizing resource parameters. Our numerical simulation shows that the range of quantum key distribution can, in principle, be markedly increased but at the expense of an atrociously unfeasible secret key-generation rate; however, the upper bound of our key rates closely approaches the Takeoka–Guha–Wilde upper bound. Our analysis demonstrates the need for new technology, such as quantum memory, to synchronize photons; our methods should serve as a valuable component for accurately modeling quantum-memory-based long-distance quantum key distribution.