Self-Testing and Device-Independent Quantum Random Number Generation with Nonmaximally Entangled States
Year: 2018
Type: dissertation
Abstract: The generation of random number sequences, that is, of unpredictable sequences free from any structure, has found numerous applications in the field of information technologies. One of the most sensitive applications is cryptography, whose modern practice makes use of secret keys that must indeed be unpredictable for any potential adversary. This type of application demands highly secure randomness generators.This thesis contributes to the device-independent approach to quantum random number generation (DIRNG, for Device-Independent Random Number Generation). Those methods of randomness generation exploit the fundamental unpredictability of the measurement of quantum systems. In particular, the security of device-independent methods does not appeal to a specific model of the device itself, which is treated as a black box. This approach therefore stands in contrast to more traditional methods whose security rests on a precise theoretical model of the device, which may lead to vulnerabilities caused by hardware malfunctions or tampering by an adversary.Our contributions are the following. We first introduce a family of robust self-testing criteria for a class of quantum systems that involve partially entangled qubit pairs. This powerful form of inference allows us to certify that the contents of a quantum black box conforms to one of those systems, on the sole basis of macroscopically observable statistical properties of the black box.That result leads us to introduce and prove the security of a protocol for randomness generation based on such partially entangled black boxes. The advantage of this method resides in its low shared entanglement cost, which allows to reduce the use of quantum resources (both entanglement and quantum communication) compared to existing DIRNG protocols.We also present a protocol for randomness generation based on an original estimation of the black-box correlations. Contrary to existing DIRNG methods, which summarize the accumulated measurement data into a single quantity---the violation of a unique Bell inequality---, our method exploits a complete, multidimensional description of the black-box correlations that allows it to certify more randomness from the same number of measurements. We illustrate our results on a numerical simulation of the protocol using partially entangled states.
Author: Bamps, Cédric
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7015214337