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Centre for Quantum Information and Foundations

 

Schedule    

This 16 lecture course will be taught in Lent term 2022.

Course summary   

The course gives an introduction to foundational questions in quantum theory
and quantum information, with a focus on the relationship between quantum
theory and gravity.  We will examine arguments that the gravitational field
must necessarily be quantized, together with counter-arguments,
review old ideas of semi-classical theories of gravity and
their problems, and discuss recently proposed experiments that
aim to use the properties of quantum information to
test whether gravity is indeed mediated by quantum particle exchange.

Topics covered in the course will include:

Basic concepts in quantum theory and quantum information: pure and mixed states,
  density matrix, the Schmidt decomposition, entanglement, the no-cloning theorem.
Relationship between quantum theory and relativity: the no-signalling principle;
quantum state summoning and the no-summoning theorem; possible and impossible summoning tasks.

  • Bell's theorem and Bell nonlocality.   
  • Entanglement measures and entanglement witnesses.
  • Everettian quantum theory and collapse-based versions of quantum theory.
  • Basic notions of semi-classical gravity; the Page-Geilker experiment.
  • Quantum theory and gravity: the Colella, Overhauser and Werner experiment; the Eppley-Hannah argument.
  • Non-linear extensions of quantum theory; refutation of the Eppley-Hannah argument
  • The proposed experiments of Bose et al. and Marletto-Vedral testing the generation of entanglement between separated mesoscopic quantum systems in superposition.
  • Discussion of what positive or negative results in BMV experiments would imply.

If time permits we may also discuss other recent experimental proposals.

Course prerequisites

Familiarity with undergraduate level quantum mechanics is essential.
Familiarity with a first course in quantum information theory, such as the Cambridge
Part II Quantum Information and Computation course, would be highly
advantageous.