In this work our aim has been to elucidate our theoretical developments that bolster the efficiency of quantum key distribution systems leading to more secure communication channels, as well as develop rigorous methods for their analysis. After a review of the necessary mathematical and physical preliminaries and a discussion of the present state of quantum communication technologies, we begin by investigating the Trojan Horse Attack, a form of side-channel attack that could threaten the security of existing key distribution protocols. We examine the secret key rates that may be achieved when an eavesdropper may use any Gaussian state in the presence of thermal noise, and prove that the coherent state is optimal in this case. We then allow the eavesdropper to use any separable state, and show that this gives a key rate bound close to that of the coherent state. \n \nWe develop a protocol for a quantum repeater that makes use of the double-heralding procedure for entanglement-generation. In our analysis, we include statistical effects on the key rate arising from probabilistic entanglement generation, which results in some quantum memories decohering while other sections complete their entanglement generation attempts. We show that this results in secure communication being possible over thousands of kilometres, allowing for intercontinental key distribution. \n \nFinally, we investigate in more depth the statistical issues that arise in general quantum repeater networks. We develop a framework based on Markov chains and probability generating functions, to show how one may easily calculate an analytic expression for the completion time of a probabilistic process. We then extend this method to show how one may track the distribution of the number of errors that accrue in operating such a process. We apply these methods to a typical quantum repeater network to get new tight bounds on the achievable key rates.
In this work our aim has been to elucidate our theoretical developments that bolster the efficiency of quantum key distribution systems leading to more secure communication channels, as well as develop rigorous methods for their analysis. After a review of the necessary mathematical and physical preliminaries and a discussion of the present state of quantum communication technologies, we begin by investigating the Trojan Horse Attack, a form of side-channel attack that could threaten the security of existing key distribution protocols. We examine the secret key rates that may be achieved when an eavesdropper may use any Gaussian state in the presence of thermal noise, and prove that the coherent state is optimal in this case. We then allow the eavesdropper to use any separable state, and show that this gives a key rate bound close to that of the coherent state. \n \nWe develop a protocol for a quantum repeater that makes use of the double-heralding procedure for entanglement-generation. In our analysis, we include statistical effects on the key rate arising from probabilistic entanglement generation, which results in some quantum memories decohering while other sections complete their entanglement generation attempts. We show that this results in secure communication being possible over thousands of kilometres, allowing for intercontinental key distribution. \n \nFinally, we investigate in more depth the statistical issues that arise in general quantum repeater networks. We develop a framework based on Markov chains and probability generating functions, to show how one may easily calculate an analytic expression for the completion time of a probabilistic process. We then extend this method to show how one may track the distribution of the number of errors that accrue in operating such a process. We apply these methods to a typical quantum repeater network to get new tight bounds on the achievable key rates.
We develop techniques to analyze the statistics of completion times of nondeterministic elements in quantum-entanglement generation and how they affect the overall performance as measured by the secret key rate. By considering such processes as Markov chains, we show how to obtain exact expressions for the probability distributions over the number of errors that a network acquires, as well as the distribution of entanglement establishment times. We show how results from complex analysis can be used to analyze Markov matrices to extract information with a lower computational complexity than previous methods. We apply these techniques to the Briegel et al. quantum repeater protocol [H.-J. Briegel et al., Phys. Rev. Lett. 81, 5932 (1998)] and find that consideration of the effect of statistical fluctuations can tighten bounds on the secret key rate by three orders of magnitude, when compared to more simplistic analyses. We also use the theory of order statistics to derive tighter bounds on the minimum quantum memory lifetimes that are required in order to communicate securely.
Quantum key distribution (QKD) can be proved to be secure by laws of quantum mechanics. In this thesis, we review security proof methods in Renner's framework and discuss numerical methods to calculate asymptotic and finite key rates. These methods are highly versatile and applicable to general device-dependent QKD protocols. We also discuss analytical tools that extend the applicability of these numerical methods. We then present the asymptotic security proof against collective attacks for a variant of the twin-field QKD protocol, which can overcome the repeaterless secret-key capacity bound. Our variant reduces the sifting cost and uses non-phase-randomized coherent states as both signals and test states. We confirm the loss scaling of this protocol. Another important family of protocols that we investigate here are discrete-modulated continuous-variable QKD protocols. They are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks. Our security proof method can provide tight asymptotic key rates. We demonstrate that the postselection of data in combination with reverse reconciliation can improve the key rates. We analyze both untrusted and trusted detector noise scenarios. Our results in the trusted detector noise scenario show that we can thus cut out most of the effect of detector noise and obtain asymptotic key rates similar to those had we access to ideal detectors. Finally, we present several simple examples to illustrate our newly developed method for the numerical finite-key analysis against the most general attacks via the entropy accumulation theorem.
Quantum key distribution over probabilistic quantum repeaters is addressed. We compare, under practical assumptions, two such schemes in terms of their secret key generation rates per quantum memory. The two schemes under investigation are the one proposed by Duan et al. [Nature (London) 414, 413 (2001)] and that of Sangouard et al. [Phys. Rev. A 76, 050301 (2007)]. We consider various sources of imperfection in both protocols, such as nonzero double-photon probabilities at the sources, dark counts in detectors, and inefficiencies in the channel, photodetectors, and memories. We also consider memory decay and dephasing processes in our analysis. For the latter system, we determine the maximum value of the double-photon probability beyond which secret key distillation is not possible. We also find crossover distances for one nesting level to its subsequent one. We finally compare the two protocols in terms of their achievable secret key generation rates at their optimal settings. Our results specify regimes of operation where one system outperforms the other.
The discrete-variable quantum key distribution protocols based on the 1984 protocol of Bennett and Brassard (BB84) are known to be secure against an eavesdropper, Eve, intercepting the flying qubits and performing any quantum operation on them. However, these protocols may still be vulnerable to side-channel attacks. We investigate the Trojan-horse side-channel attack where Eve sends her own state into Alice's apparatus and measures the reflected state to estimate the key. We prove that the separable coherent state is optimal for Eve among the class of multimode Gaussian attack states, even in the presence of thermal noise. We then provide a bound on the secret key rate in the case where Eve may use any separable state.
Quantum Key Distribution (QKD) represents a revolutionary approach in the field of cryptography, offering the potential for unconditional security by leveraging the principles of quantum mechanics. This paper addresses the crucial issue of calculating secure key rates in entanglement based QKD systems. We present a method of key rate calculations that is independent of an eavesdropper's quantum system, relying solely on the quantum states shared between two communicating parties under the assumption of a worst-case attack. We undertake a comparison of asymptotic key rates with those observed in the finite regime, in which only a limited number of quantum states are exchanged. Furthermore, we investigate the influence of entanglement distillation on the achievable key rates. By identifying the numerically optimal number of entanglement distillation iterations based on the initial fidelity and the number of exchanged quantum states, we demonstrate how to achieve a balance between the quantity and quality of entangled states, thereby maximizing the secure key rate. Our results show that there is a unique optimum within a defined search range. Moreover, we determine the minimum number of exchanged quantum states necessary to attain a positive key rate and to obtain a desired number of secure key bits, which are both contingent upon the quality of the communication channel. It is anticipated that the insights gained from this work will prove instrumental in the development of optimal routing strategies in quantum communication networks.
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.