Quantum key security : theory and analysis of experimental realisations

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Reconciliation for Satellite-Based Quantum Key Distribution

This thesis reports on reconciliation schemes based on Low-Density Parity-Check (LDPC) codes in Quantum Key Distribution (QKD) protocols. It particularly focuses on a trade-off between the complexity of such reconciliation schemes and the QKD key growth, a trade-off that is critical to QKD system deployments. A key outcome of the thesis is a design of optimised schemes that maximise the QKD key growth based on finite-size keys for a range of QKD protocols. Beyond this design, the other four main contributions of the thesis are summarised as follows. First, I show that standardised short-length LDPC codes can be used for a special Discrete Variable QKD (DV-QKD) protocol and highlight the trade-off between the secret key throughput and the communication latency in space-based implementations. Second, I compare the decoding time and secret key rate performances between typical LDPC-based rate-adaptive and non-adaptive schemes for different channel conditions and show that the design of Mother codes for the rate-adaptive schemes is critical but remains an open question. Third, I demonstrate a novel design strategy that minimises the probability of the reconciliation process being the bottleneck of the overall DV-QKD system whilst achieving a target QKD rate (in bits per second) with a target ceiling on the failure probability with customised LDPC codes. Fourth, in the context of Continuous Variable QKD (CV-QKD), I construct an in-depth optimisation analysis taking both the security and the reconciliation complexity into account. The outcome of the last contribution leads to a reconciliation scheme delivering the highest secret key rate for a given processor speed which allows for the optimal solution to CV-QKD reconciliation

Assumptions in Quantum Cryptography

Quantum cryptography uses techniques and ideas from physics and computer science. The combination of these ideas makes the security proofs of quantum cryptography a complicated task. To prove that a quantum-cryptography protocol is secure, assumptions are made about the protocol and its devices. If these assumptions are not justified in an implementation then an eavesdropper may break the security of the protocol. Therefore, security is crucially dependent on which assumptions are made and how justified the assumptions are in an implementation of the protocol. This thesis is primarily a review that analyzes and clarifies the connection between the security proofs of quantum-cryptography protocols and their experimental implementations. In particular, we focus on quantum key distribution: the task of distributing a secret random key between two parties. We provide a comprehensive introduction to several concepts: quantum mechanics using the density operator formalism, quantum cryptography, and quantum key distribution. We define security for quantum key distribution and outline several mathematical techniques that can either be used to prove security or simplify security proofs. In addition, we analyze the assumptions made in quantum cryptography and how they may or may not be justified in implementations. Along with the review, we propose a framework that decomposes quantum-key-distribution protocols and their assumptions into several classes. Protocol classes can be used to clarify which proof techniques apply to which kinds of protocols. Assumption classes can be used to specify which assumptions are justified in implementations and which could be exploited by an eavesdropper. Two contributions of the author are discussed: the security proofs of two two-way quantum-key-distribution protocols and an intuitive proof of the data-processing inequality.Comment: PhD Thesis, 221 page

Schrodinger wave-mechanics and large scale structure

In recent years various authors have developed a new numerical approach to cosmological simulations that formulates the equations describing large scale structure (LSS) formation within a quantum mechanical framework. This method couples the Schrodinger and Poisson equations. Previously, work has evolved mainly along two different strands of thought: (1) solving the full system of equations as Widrow & Kaiser attempted, (2) as an approximation to the full set of equations (the Free Particle Approximation developed by Coles, Spencer and Short). It has been suggested that this approach can be considered in two ways: (1) as a purely classical system that includes more physics than just gravity, or (2) as the representation of a dark matter field, perhaps an Axion field, where the de Broglie wavelength of the particles is large. In the quasi-linear regime, the Free Particle Approximation (FPA) is amenable to exact solution via standard techniques from the quantum mechanics literature. However, this method breaks down in the fully non-linear regime when shell crossing occurs (confer the Zel'dovich approximation). The first eighteen months of my PhD involved investigating the performance of illustrative 1-D and 3-D ``toy" models, as well as a test against the 3-D code Hydra. Much of this work is a reproduction of the work of Short, and I was able to verify and confirm his results. As an extension to his work I introduced a way of calculating the velocity via the probability current rather than using a phase unwrapping technique. Using the probability current deals directly with the wavefunction and provides a faster method of calculation in three dimensions. After working on the FPA I went on to develop a cosmological code that did not approximate the Schrodinger-Poisson system. The final code considered the full Schrodinger equation with the inclusion of a self-consistent gravitational potential via the Poisson equation. This method follows on from Widrow & Kaiser but extends their method from 2D to 3D, it includes periodic boundary conditions, and cosmological expansion. Widrow & Kaiser provided expansion via a change of variables in their Schrodinger equation; however, this was specific only to the Einstein-de Sitter model. In this thesis I provide a generalization of that approach which works for any flat universe that obeys the Robertson-Walker metric. In this thesis I aim to provide a comprehensive review of the FPA and of the Widrow-Kaiser method. I hope this work serves as an easy first point of contact to the wave-mechanical approach to LSS and that this work also serves as a solid reference point for all future research in this new field

Information-theoretic security under computational, bandwidth, and randomization constraints

The objective of the proposed research is to develop and analyze coding schemes for information-theoretic security, which could bridge a gap between theory an practice. We focus on two fundamental models for information-theoretic security: secret-key generation for a source model and secure communication over the wire-tap channel. Many results for these models only provide existence of codes, and few attempts have been made to design practical schemes. The schemes we would like to propose should account for practical constraints. Specifically, we formulate the following constraints to avoid oversimplifying the problems. We should assume: (1) computationally bounded legitimate users and not solely rely on proofs showing existence of code with exponential complexity in the block-length; (2) a rate-limited public communication channel for the secret-key generation model, to account for bandwidth constraints; (3) a non-uniform and rate-limited source of randomness at the encoder for the wire-tap channel model, since a perfectly uniform and rate-unlimited source of randomness might be an expensive resource. Our work focuses on developing schemes for secret-key generation and the wire-tap channel that satisfy subsets of the aforementioned constraints.Ph.D

Information reconciliation methods in secret key distribution

We consider in this thesis the problem of information reconciliation in the context of secret key distillation between two legitimate parties. In some scenarios of interest this problem can be advantageously solved with low density parity check (LDPC) codes optimized for the binary symmetric channel. In particular, we demonstrate that our method leads to a significant efficiency improvement, with respect to earlier interactive reconciliation methods. We propose a protocol based on LDPC codes that can be adapted to changes in the communication channel extending the original source. The efficiency of our protocol is only limited by the quality of the code and, while transmitting more information than needed to reconcile Alice’s and Bob’s sequences, it does not reveal any more information on the original source than an ad-hoc code would have revealed.---ABSTRACT---En esta tesis estudiamos el problema de la reconciliación de información en el contexto de la destilación de secreto entre dos partes. En algunos escenarios de interés, códigos de baja densidad de ecuaciones de paridad (LDPC) adaptados al canal binario simétrico ofrecen una buena solución al problema estudiado. Demostramos que nuestro método mejora significativamente la eficiencia de la reconciliación. Proponemos un protocolo basado en códigos LDPC que puede ser adaptado a cambios en el canal de comunicaciones mediante una extensión de la fuente original. La eficiencia de nuestro protocolo está limitada exclusivamente por el código utilizado y no revela información adicional sobre la fuente original que la que un código con la tasa de información adaptada habría revelado

Advanced techniques for continuous-variable quantum communications over the atmosphere

This thesis analyses the application of various techniques to enhance the free-space transmission of Continuous-Variable (CV) quantum communications via the atmosphere. The techniques studied encompass a wide range of methods, from classical techniques to entanglement distillation and quantum error correction. A new realistic model of the atmospheric quantum channel is constructed. This model simulates the detrimental effects incurred on quantum information as it traverses the atmosphere. The model allows us to determine the feasibility of satellite-based quantum communications and develop new techniques to enhance free-space CV quantum communication. Entanglement distillation via non-Gaussian operations is analyzed to enhance Quantum Key Distribution and quantum teleportation in satellite-based quantum communications. While many non-Gaussian states exist, their use to obtain an advantage in any quantum communications protocol depends on the specifics of the quantum state and the channel involved in the quantum communications. Determination of which non-Gaussian states and the conditions in which such an advantage can be obtained in the context of free-space transmission is one of the contributions of this thesis. In satellite-based communications, the uplink channel is considerably more destructive than the downlink channel. A new technique for uplink state transfer that improves transmission by employing quantum teleportation via the downlink channel is introduced in this thesis. In line with the theme of this thesis, the enhancement of this technique using non-Gaussian entangled states during quantum teleportation is also analyzed. Finally, a protocol to perform error correction applied to the free-space transmission of quantum information is presented. In this protocol, quantum information transfer can be augmented by carefully monitoring the free space channel and following an optimization process. This thesis provides novel and significant developments that can be applied to advance CV quantum communications through the atmosphere for satellite-based and ground-level horizontal communications. Such developments should prove beneficial for realizing the future global quantum internet