Year: 2017
Type: dissertation
Abstract: The field of quantum computing investigates the extent to which one can design a quantum system that outperforms all known classical hardware at a certain task.But, to what extent can a human being, capable only (perhaps) of classical computation and of observing classical bit-string messages, verify that a quantum device in their possession is performing the task that they wish?This is a fundamental question about the nature of quantum mechanics, and the extent to which humans can harness it in a trustworthy manner.It is also a natural and important consideration when quantum devices may be used to perform sensitive cryptographic tasks which have no known efficient classical witness of correctness (Quantum Key Distribution, and Randomness Expansion are two examples of such tasks).It is remarkable that any quantum behavior at all can be tested by a verifier under such a constraint, without trusting any other quantum mechanical device in the process!But, intriguingly, when there are two or more quantum provers available in an interactive proof, there exist protocols to verify many interesting and useful quantum tasks in this setting.This thesis investigates multi-prover interactive proofs for verifying quantum behavior, and focuses on the stringent testing scenario in which the verifier in the interactive proof is completely classical as described above.It resolves the question of the maximum attainable expansion rate of a randomness expansion protocol by providing an adaptive randomness expansion protocol that achieves an arbitrary, or infinite rate of randomness expansion [29].Secondly it presents a new rigidity result for the parallel repeated magic square game [24], which provides some improvements on previous rigidity results that play a pivotal role in existing interactive proofs for entangled provers, QKD, and randomness expansion results.This new rigidity result may be useful for improving such interactive proofs in the future.The second half of this thesis investigates the problem of bounding the role of quantum The further I go the more I value what my parents' example has taught me, not about science, but about life.I love you Mom and Dad.My deep gratitude goes to my advisor, Peter Shor, for guidance in research throughout graduate school, and for supporting my own research endeavors.During a PhD a student's mind is full of many different considerations, both scientific and logistical.Peter's advice is an invaluable way to refocus on the heart of the research problem at hand and, with stunning consistency, to learn something amazing and new.During my PhD I have had the privilege of collaborating with many talented researchers and good friends.What would the exploration process be without people share ideas with, and fellow researchers with which to share the thrill of discovery?Many thanks to my collaborators (listed here in no particular order)!I can only hope to continue to have such great collaborations again in the future:
Author: Matthew Coudron
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2766280656