Foundations of quantum theory and quantum information applications

TL;DR

This thesis explores the foundational aspects of quantum theory and their implications for quantum information applications, including protocols, entanglement, and quantum communication, providing new insights and experimental conditions.

Contribution

It establishes connections between quantum foundations and information protocols, deriving conditions for tests, and analyzing entanglement and quantum communication advantages.

Findings

Quantum non-locality and contextuality are crucial for specific quantum protocols.

Conditions for experimental tests of quantum properties are derived.

Single-qubit communication can replace large classical communication, with experimental feasibility.

Abstract

This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement characterisation, and of a few quantum information protocols. Quantum non-locality and contextuality are shown to be essential for different implementations of quantum information protocols known as quantum random access codes and quantum communication complexity protocols. I derive sufficient experimental conditions for tests of these quantum properties. I also discuss how the distribution of quantum information through quantum cloning processes can be useful in quantum computing. Regarding entanglement characterisation, some results are obtained relating two problems, that of additivity of the relative entropy of entanglement, and that of identifying different types of tripartite entanglement in the asymptotic regime of manipulations of many copies of a given state. The thesis ends with a description of an information processing task in which a single qubit substitutes for an arbitrarily large amount of classical communication. This result is interpreted in different ways: as a gap between quantum and classical computation space complexity; as a bound on the amount of classical communication necessary to simulate entanglement; and as a basic result on hidden-variable theories for quantum mechanics. I also show that the advantage of quantum over classical communication can be established in a feasible experiment.