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The Statistics and Security of Quantum Key Distribution

Vinay, Scott (2018) The Statistics and Security of Quantum Key Distribution. PhD thesis, University of Sheffield.

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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. We 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. Finally, 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.

Item Type: Thesis (PhD)
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > Physics and Astronomy (Sheffield)
Identification Number/EthosID: uk.bl.ethos.784684
Depositing User: Mr Scott Vinay
Date Deposited: 10 Sep 2019 09:06
Last Modified: 25 Sep 2019 20:08
URI: http://etheses.whiterose.ac.uk/id/eprint/24610

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