Public defence in Mathematics and Statistics, M.Sc. Matteo Allaix
Title of the doctoral thesis: Quantum Private Information Retrieval from Coded Storage Systems
Doctoral student: Matteo Allaix
Opponent: Prof. Alberto Ravagnani, Eindhoven University of Technology, the Netherlands
Custos: Prof. Camilla Hollanti, Aalto University School of Science, Department of Mathematics and Systems Analysis
Thesis available for public display 10 days prior to the defence at:
The problem of Quantum Private Information Retrieval (QPIR) aims to address the privacy concerns of the modern digitalized world, where any leak of your personal data might be used to inflict some personal harm or utilized toward economical benefit without appropriate compensation.
In the thesis, we focus on the setting of QPIR from coded distributed storage systems: a distributed storage system is a set of hardware components, usually handled by some software, that is designed to store, organize, and manage digital data; a coded storage system stores encoded data to prevent data loss, minimize downtime, and protect against potential disruptions; private information retrieval is the process of downloading data from a storage system while keeping the identity of the requested file private to the user; quantum refers to the fact that we enable quantum communication in the process to provide more secure transmission of data and faster retrieval for specific problems compared to classical protocols.
In the thesis, we propose the first examples of QPIR protocols from storage systems encoded with non-trivial codes (for example Reed-Solomon polynomial evaluation codes), and we show that one of the proposed protocols is the best possible one in terms of the amount of downloaded data vs. the size of the requested file. The proposed protocols are information-theoretically secure, meaning that they are also post-quantum secure as they do not rely on computational hardness. Furthermore, we extract the core tool as a classical "black box" with quantum functionality as a so-called N-sum box using the properties of quantum error-correction codes. In other words, this black box is a tool that takes 2N numbers as input and gives N sums of those 2N numbers as output. This means that non-quantum researchers can apply the N-sum box to improve classical protocols over many-to-one networks without the need to know the specifics of the quantum functionality.
As mentioned above, quantum communication provides improvements only for specific problems, including QPIR studied in this thesis. Quantum computation and communication have the potential to revolutionize the digital world as we know it, but they also have some strong limitations that make such a revolution much more challenging to achieve.
Doctoral theses in the School of Science: https://aaltodoc.aalto.fi/handle/123456789/52