Quantum Key Distribution (QKD) has opened a new avenue for secure communication, by allowing one to distribute a random secret key between two users that are connected through a public channel without revealing information to unauthorized parties. If a message is encrypted with the one time pad (a well-known crytography algorithm) using secret keys created by QKD, then the ciphertext is information-theoretically secure and thus unbreakable for adversaries. Despite its unprecedented security, loss in the physical channel has prevented QKD from being used over distances beyond a few hundred kilometers. Fortunately, quantum repeaters have opened a path for long-distance QKD by providing a means to establish entanglement between distant users. The goal of this thesis has been to develop a source of entangled photon pairs that is suitable for quantum repeaters and then use it to test some of the fundamental building blocks of a quantum repeater : the heralded creation of entangled photons by means of entanglement swapping with properties that allow interfacing with optical quantum memories; the reversible mapping of quantum states from members of entangled photon pairs in and out of solid-state quantum memories; two-photon interference and a Bell state measurement with photons recalled from separate quantum memories. The demonstration of these key ingredients of a quantum repeater constitutes a significant step towards the establishment of entanglement over hundreds of kilometer distance, and hence long-distance QKD.
Quantum Key Distribution (QKD) has opened a new avenue for secure communication, by allowing one to distribute a random secret key between two users that are connected through a public channel without revealing information to unauthorized parties. If a message is encrypted with the one time pad (a well-known crytography algorithm) using secret keys created by QKD, then the ciphertext is information-theoretically secure and thus unbreakable for adversaries. Despite its unprecedented security, loss in the physical channel has prevented QKD from being used over distances beyond a few hundred kilometers. Fortunately, quantum repeaters have opened a path for long-distance QKD by providing a means to establish entanglement between distant users. The goal of this thesis has been to develop a source of entangled photon pairs that is suitable for quantum repeaters and then use it to test some of the fundamental building blocks of a quantum repeater : the heralded creation of entangled photons by means of entanglement swapping with properties that allow interfacing with optical quantum memories; the reversible mapping of quantum states from members of entangled photon pairs in and out of solid-state quantum memories; two-photon interference and a Bell state measurement with photons recalled from separate quantum memories. The demonstration of these key ingredients of a quantum repeater constitutes a significant step towards the establishment of entanglement over hundreds of kilometer distance, and hence long-distance QKD.
"Quantum communication is the art of transferring a quantum state from one place to another". The capability of distributing quantum states allows, for instance, provably secure communication and, in the near future, will enable the interconnection of quantum computers to establish a quantum internet. A convenient way to send quantum states from one place to another is to encode them into photons and distribute them using optical bres. The distance over which this can be achieved is still limited to a few hundred of kilometers. However, it can be extended in principle to arbitrary long distances by means of quantum repeaters. The realization of such quantum repeaters will require the engineering and interfacing of heterogeneous elements such as entangled photon-pair sources, quantum memories and entanglement swapping operations. The main goal of this thesis is to develop and study the compatibility of the main elements required to build a frequency multiplexed quantum repeater. This architecture requires a frequency multimode entangled photon pair source which, for example, could be implemented exploiting the process that involves the interaction of a strong light pulse with a non-linear crystal. Such a process is versatile and allows easy tailoring of the photon-pair spectral properties in order to match the requirements of the frequency multiplexed quantum repeater architecture. First, as a precursor of such a photon pair source, we developed a novel heralded single photon source that involves spectrally resolved single photon detection and on-demand frequency shifting. These capabilities are also essential tools in a frequency multiplexed quantum repeater. Next, we demonstrated the compatibility of such a sources with frequency multimode photonic quantum memories by performing spectrally multiplexed storage of single photons. We also tested the capability of high- delity storage of photons encoding quantum information in their polarization degree of freedom. Finally, we showed that entanglement swapping operations, i.e. Bell-state measurements, can be performed using photon pair sources compatible with quantum memories, quantum repeater architectures, and real-world scenarios. While a lot of e ort remains to be done, in the work presented in this thesis we demonstrated that all the key elements required to build a frequency multiplexed quantum repeater can be built and eventually be interfaced. The main obstacles towards that goal and possible ways to overcome them are also discussed.
Quantum correlations arising from measurements on pairs of entangled particles are often referred to as the most non-classical feature of quantum mechanics. As such, they have found a role in many fundamental tests of quantum mechanics and most emerging applications in the field of quantum communication. The most well-known fundamental test is the Bell inequality. Its repeated violation in countless experiments has convinced physicists that local hidden variables cannot describe the correlations arising from measurements on entangled particles. On the application side, quantum correlations have been used in quantum key distribution, which aims to provably secure messages during transmission, and quantum repeaters, which are essential for future long-distance quantum communication. The main goal of this thesis was to use quantum entanglement for new fundamental studies and quantum communication applications. Towards this end, we developed a high-fidelity source of entanglement and used it in a fundamental test where we bounded the predictive power any physical theory could have about the outcomes of measurements on entangled particles. Secondly, we made use of entangling measurements to develop a new quantum cryptography system based on the promising MDI-QKD protocol, which protects users from otherwise undetectable hacking attacks. We developed a detailed model of MDI-QKD systems with which one can optimize any implementation, deployed our MDI-QKD system across the city of Calgary, and demonstrated the feasibility of this protocol and of long-distance entangling measurements. Thirdly, we have built a source of entanglement compatible with quantum memories, which is an essential ingredient of quantum repeaters. We then demonstrated several crucial steps towards a functioning quantum repeater, including the preservation of entanglement during storage and, more generally, the entire photonic wavefunction. While further work is required to bring our demonstrations to real-world applications, we are confident that they will prove useful in guiding future developments.
As children, whispering into the ear of a friend in the presence of others allows us to pass a secret without interception, and forms one of the simplest attempts at secret communications we can employ. However, sending secret messages becomes deeply nontrivial over long distances. \n \nA solution for two parties to communicate securely is to encrypt and decrypt a message with two identical strings of bits, one for each party. In this case, the security of the encrypted message is provable and does not rely on assumptions on computational power. Quantum theory provides a clear solution for the initial distribution of these identical bit strings through Quantum Key Distribution. However, once long distances are involved, the corresponding loss involved in direct transmission ruins the effectiveness of quantum key distribution by reducing the effective rate exponentially with the distance. \n \nTo circumvent the losses involved in direct transmission, quantum repeater architectures have been proposed. We present our contributions towards three aspects of quantum repeater systems in this thesis. We ensure conditions for implementing quantum repeaters with atomic ensembles, explore the option of optomechanical systems for implementing quantum repeaters and verify the success of completed quantum repeater protocols. \n \nIn the first part of this thesis, we show how we can ensure conditions for the successful implementation of quantum repeater systems with atomic ensembles. These quantum repeater systems are formed with 1-dimensional networks, where the nodes are made up of quantum memories connected by means of single photons. This requires memories that are highly efficient. Also, if quantum repeater systems are implemented with hybrid resources, tunable photon waveforms will be desirable. We propose a protocol to implement quantum memories with atomic ensembles using a clear recipe to optimise the efficiency. We also demonstrate that a cold ensemble of Rubidium-87 can act as an efficient tunable source of single photons, along with flexibility in the produced temporal shapes. \n \nNext, we show how we can explore alternative options for the nodes of quantum repeater systems. We focus on optomechanical oscillators, and recognise that they can also be used as quantum memories. We present a witness to certify that this memory successfully operates in the quantum regime. \n \nFinally, we focus on the verification of successfully implemented quantum repeater protocols. This verification will be essential for certifying that quantum repeater systems operate as instructed. We use only local homodyne measurements to witness the success of the network, and find that the witness is robust to loss. \n \nWe thus present distinct contributions towards three important aspects of quantum repeater systems. As far as a full-fledged quantum repeater system might seem to be right now, we have faith that our work brings the field of quantum-enabled secure communications forward.
The feasibility of trust-free long-haul quantum key distribution (QKD) is addressed. We combine measurement-device-independent QKD, as an access technology, with a quantum repeater setup, at the core of future quantum communication networks. This will provide a quantum link none of whose intermediary nodes need to be trusted, or, in our terminology, a trust-free QKD link. As the main figure of merit, we calculate the secret key generation rate when a particular probabilistic quantum repeater protocol is in use. We assume the users are equipped with imperfect single photon sources, which can possibly emit two single photons, or laser sources to implement decoy-state techniques. We consider apparatus imperfection, such as quantum efficiency and dark count of photodetectors, path loss of the channel, and writing and reading efficiencies of quantum memories. By optimizing different system parameters, we estimate the maximum distance over which users can share secret keys when a finite number of memories are employed in the repeater setup.
Quantum communications enable secure key transmission and entanglement distribution, but their rates and maximum transmission distances are limited due to the losses and noise introduced by quantum channels. Various techniques have been developed to address these limitations, tailored to the platform and the nature of the decoherence. In this thesis, we explore ways to enhance the performance of quantum communications, with a particular focus on increasing the key rates and transmission distances in quantum key distribution (QKD), a method that leverages quantum mechanics to securely share keys between trusted parties. Additionally, we aim to improve the purity of entangled states shared between two parties, contributing to broader advancements in quantum communications. We begin by introducing a software-enhanced continuous-variable QKD (CV-QKD) protocol, where keys are encoded onto the phase and amplitude degrees of the optical field. This protocol enhances both transmission distance and key rates through a post-selection method employing arbitrary filters, experimentally demonstrated on two different platforms. Its adaptability makes it highly promising, as it can be implemented on existing CV-QKD platforms and dynamically optimises key rates for rapidly changing channels. We then present a protocol for the pure-loss channel leveraging quantum repeaters to mitigate the channel losses by segmenting the total communication distance into smaller, more manageable intervals. This repeater-like protocol introduces a more efficient entanglement-swapping measurement at the repeater station than the state-of-the-art twin-field protocols. Instead of polarisation encoding, our protocol relies on encoding keys in the photon-number basis, optimising the states to achieve the highest key rates for each distance. Notably, this protocol shows strong potential for improving long-distance quantum communication by surpassing the capacity of the direct communication channel at a shorter distance than the existing repeater protocols such as twin-field QKD while achieving an overall higher transmission distance. Finally, in this thesis, we demonstrate that for the Pauli-dephasing channel, placing a node in the middle of the quantum channel to perform a Bell-state measurement as an entanglement-swapping operation does not result in improved key rates, even with reduced decoherence. As a result, we propose an entanglement purification protocol that refines a larger set of noisy entangled states into a smaller set of high-fidelity ones using local operations and classical communication. This purification protocol builds upon earlier purification methods, extending their application from two Bell pairs to any number of Bell pairs and thereby achieving the capacity of the dephasing channel. Through numerous recursive iterations, it produces near-perfect Bell pairs, making it well-suited for quantum repeaters and correcting dephasing errors in quantum computers.
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.