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Enabling secure communications: theoretical tools for quantum repeater systems

Melvyn Ho

Published Jan 1, 2018• 0 citations
Publisher

Abstract

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.

DOI
10.5451/unibas-007073321

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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.
Future quantum networks will enable the realisation of a large family of quantum protocols, hence allowing for implementation of various tasks ranging from quantum cryptography through quantum computing to quantum metrology.In this thesis we analyse and develop the building blocks of quantum repeater networks.These networks consist of quantum repeater nodes, which are equipped with quantum memories enabling storage of quantum information.The repeater nodes are connected using optical fibres that enable for the transmission of photonic quantum signals between the repeater nodes.We specifically focus on the two building blocks: remote entanglement generation and entanglement distillation.We then investigate various proof of principle quantum repeater schemes used for generating shared secret key between distant parties.The repeater schemes that we consider utilise one to three memory nodes capable of generating memory-photon entanglement.Finally, we introduce a novel framework for investigating a foundational aspect in the use of quantum communication related to the uncertainty principle.Efficient remote entanglement generation is an indispensable building block of most near-term quantum repeater networks.In this thesis we consider various remote entanglement generation schemes that permit multiplexing, which aims at increasing the throughput of this procedure.We find that for the specific schemes that are suitable for platforms with a single communication qubit and multiple memory qubits, the performance of the multiplexing approach is strongly dependent on the time it takes to perform local operations within the memory nodes.Entanglement distillation enables for filtering out the noise from imperfect entangled states using only local operations and classical communication.Using a general framework for optimising such schemes, which we have developed, we have proven optimality of specific generic and experimentally relevant distillation schemes.We have developed a general framework for optimising such schemes, which we have used to prove optimality of various generic and experimentally relevant distillation schemes.In designing proof of principle quantum repeater schemes we assume an informationtheoretic approach, which enables us to assess their performance in a hardware-agnostic way.We find that all the schemes that we consider can prove useful in specific parameter regimes for the nitrogen-vacancy centre platform.Moreover, we find that one scheme which has already been realised experimentally in the context of remote entanglement generation, is expected to significantly outperform every possible system based on direct communication without repeaters.However, our analysis shows that encapsulating the nitrogen-vacancy centres in optical cavities for the enhancement of the emission rates is a necessary requirement for such a successful demonstration of the first proofof-principle quantum repeater.xi xii SUMMARY Finally, we investigate the quantum uncertainty principle which is a fundamental feature of quantum mechanics, allowing for security in many quantum cryptographic protocols.We find that in a particular scenario, relevant from the perspective of quantum key distribution, a significant part of the observed uncertainty is in fact due to lack of information rather than intrinsic.If the eavesdropper could access that information, she would be able to much better, or in some cases even with certainty, guess the value of the raw bit of the generated key.
This thesis is an exploration of quantum repeaters from a practical point of view. Quantum repeaters are devices which help improve the quantum communication capacity of a lossy bosonic channel (which include photonic channels such as optical fiber) beyond what is possible using a purely lossy channel. The analyses in this thesis involve modeling the experimental imperfections inherent in the various devices which comprise a quantum repeater, then combining these models to calculate various quantities of interest. \n \nTwo systems are analyzed in this thesis. One is a simple quantum repeater, while the other is a potential building block for more complex quantum repeaters. \n \nThe simple quantum repeater scheme can be implemented with currently available technology. In it, two parties perform quantum key distribution (QKD) by exchanging photons with two quantum memories placed between them. Its secret key rate ideally scales as the square root of the transmittivity of the optical channel, which is superior to QKD schemes based on direct transmission because key rates for the latter scale at best linearly with transmittivity. Taking into account imperfections in the setup, such as detector efficiency and dark counts, we present parameter regimes in which our protocol outperforms protocols based on direct transmission. We find that implementing our scheme with trapped ions is a promising way to reach the necessary parameter regimes, and that the regimes are easier to reach if the optical channels are very lossy. \n \nThe creation of entanglement between two quantum memories is an important building block in some quantum repeater schemes. We consider a specific quantum memory consisting of an atom trapped in a cavity. The system allows a CNOT operation to be performed between an atom and a photon. We study three methods for taking advantage of this to entangle two atoms: (1) interacting a coherent pulse with each atom, then performing an entangling measurement on the pulses; (2) interacting a single coherent pulse with each atom sequentially; (3) emitting an entangled photon from one atom and interacting it with the other atom. The success probability of each method is compared, as well as the quality of the entangled states produced by each one, taking into account imperfections which appear in a specific experimental implementation of such memories. We find that there is a tradeoff between success probability and entangled state quality when coherent states are used, and that method 3 provides higher-quality entangled states than is possible with the other two methods.
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.
Future quantum networks will enable fascinating applications such as secure communication, quantum-enhanced distributed sensing, distributed quantum computing, and accurate global timekeeping. Center to these applications is quantum entanglement distribution, whose effective distance is limited by photon loss. Quantum repeaters were proposed to extend the effective distance, but their demonstration has not been reported yet. In this thesis, we study quantum repeaters with both single-emitter based and ensemble-based quantum memories. In particular, we study the feasibility of meaningful proof-of-principle demonstrations of several quantum repeater protocols (with two-links) with photon (single-photon and photon-pair) sources and atomic-ensemble based quantum memories. We take into account non-unit memory efficiencies that decay exponentially with time, which is more realistic and accurate compared to previous treatments. We discuss implementations based on quantum dots, parametric down-conversion, rare-earth-ion doped crystals, and Rydberg atoms. Our results provide guidance for the near-term implementation of long-distance quantum repeater demonstrations, suggesting that such demonstrations are within reach of current technology.
The distribution of quantum states over long distances is limited by photon loss. Straightforward amplification as in classical telecommunications is not an option in quantum communication because of the no-cloning theorem. This problem could be overcome by implementing quantum repeater protocols, which create long-distance entanglement from shorter-distance entanglement via entanglement swapping. Such protocols require the capacity to create entanglement in a heralded fashion, to store it in quantum memories, and to swap it. One attractive general strategy for realizing quantum repeaters is based on the use of atomic ensembles as quantum memories, in combination with linear optical techniques and photon counting to perform all required operations. Here we review the theoretical and experimental status quo of this very active field. We compare the potential of different approaches quantitatively, with a focus on the most immediate goal of outperforming the direct transmission of photons.
The distribution of quantum states over long distances is limited by photon loss. Straightforward amplification as in classical telecommunications is not an option in quantum communication because of the no-cloning theorem. This problem could be overcome by implementing quantum repeater protocols, which create long-distance entanglement from shorter-distance entanglement via entanglement swapping. Such protocols require the capacity to create entanglement in a heralded fashion, to store it in quantum memories, and to swap it. One attractive general strategy for realizing quantum repeaters is based on the use of atomic ensembles as quantum memories, in combination with linear optical techniques and photon counting to perform all required operations. Here the theoretical and experimental status quo of this very active field are reviewed. The potentials of different approaches are compared quantitatively, with a focus on the most immediate goal of outperforming the direct transmission of photons.