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Quantum Cryptography with Partially Trusted Devices

par Van Himbeeck, Thomas
Président du jury Cerf, Nicolas
Promoteur Pironio, Stefano
Publication Non publié, 2019-11-04

Thèse de doctorat

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Résumé :

The aim of this thesis is the introduction of new practical Quantum Random Number Generators and new mathematical techniques to certify the random nature of the numbers, based only on a partial characterisation of the devices. Random numbers have a lot of applications, going from mathematical algorithms and betting games to cryptographic protocols, where random keys are a basic premise for constructing protocols. Random Number Generators of the Quantum type have the advantage that they rely on truly random processes, which are guaranteed to be unpredictable by the laws of physics. This makes them in principle more safe than classical hardware generators and pseudo-random algorithms. In the first part of the thesis, we focus of the task of certifying randomness. We introduce a new framework for certifying generators based on quantum optics and that follow a Prepare-and-Measure setup consisting of a source and a measurement device, such as a laser and a single photon detector. Our framework is called semi-Device-Independent, because the device is left largely uncharacterised, as no assumption is made on the source and the measurement device, except for a single physical assumption on the mean photon number (or the energy) of the states prepared by the source. This approach is very secure and robust because any malfunctioning or imperfections in the generator, such additional classical noise, are automatically taken into account as long as the energy assumption is satisfied. We show that, under an energy constraint, there is a fundamental relation between the amount of correlation between the two devices and the amount of randomness produced during the measurement. We establish this by considering all possible underlying quantum models of the devices, that satisfy the mean photon number constraint. We demonstrate that certain strong correlations indeed cannot be reproduced by an underlying deterministic model and show how to compute the amount of randomness in these cases. We then prove the security of a random number generation protocol and demonstrate it in a proof-of-principle experiment. In the second part of the thesis, we study the Instrumental scenario, which is a Device-Independent framework based on causal constraints. We derive the existence of analogues to Bell-inequalities which bound the set of classical correlations and we show that they can be violated by quantum devices. At a more fundamental level, the Instrumental scenario is interesting because it is the simplest causal scenario admitting a separation between classical and quantum correlations.