Logic and Quantum Information

Lecture 1: Logic and Quantum Information I
Lecture 2: Logic and Quantum Information II
Lecture 3: Logic and Quantum Information III
Lecture 4: Logic and Quantum Information IV
Lecture 5: Logic and Quantum Information V

This series of talks is part of the Logical Structures in Computation Boot Camp. Videos for each talk area will be available through the links above.

Speaker: Samson Abramsky (University of Oxford)

The material will be in five main parts.  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.

Part 1: 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.

Part 2: 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.

Part 3: Quantitative Features
Quantifying contextuality, contextuality as a resource for quantum advantage, macroscopic averaging and monogamy of contextuality, classication of entangled states by degree of non- locality.

Part 4: The Topological Structure of Non-Locality and Contextuality
We shall explore the rich mathematical structures underlying these concepts. The study of non-locality and contextuality can be expressed in a unified and generalised topological form in the language of sheaves or bundles, in terms of obstructions to global sections. These obstructions can, in many cases, be witnessed by cohomology invariants.

Part 5: 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.