[updated on 2014.07.07]
Instructor: Samson Abramsky (Oxford University)
Title: Logic and Quantum Information
We will present an introduction to some ideas in quantum information and foundations, emphasising logical and structural aspects. The aim is to understand how quantum mechanics requires a radical revision to our view of the nature of physical reality, while at the same time opening up new possibilities in the informatic realm. The main emphasis will be the concepts of nonlocality, contextuality and entanglement.
We will attempt to keep the prerequisites to a minimum. The course will begin with a review of some basic material.
The material will be in four main parts.
1. Review of background in discrete mathematics and probability.
The classical deterministic world: sets and functions.
The classical non-deterministic world: sets and relations.
The classical probabilistic world: discrete probability.
2. Observational scenarios. Basic notions of contextuality and non-locality.
A logical approach to Bell inequalities.
Logical forms of contextuality and non-locality, a hierarchy of these notions.
3. Quantum resources. From bit to qubits. Basic features of finite dimensional quantum mechanics.
Quantum realisations of empirical systems.
Examples where quantum resources exceed the capabilities of classical systems.
The broader world of no-signalling theories.
4. Contextuality in the classical world. Links between the contextual structures developed in the previous parts of the course and classical computation, including relational databases, constraints, and natural language semantics.