In recent decades, there has been a great renaissance of interest among theoretical physicists in foundational issues in quantum theory. As well as deepening our understanding of quantum theory and of its possible relationship to cosmology and gravity, this work has had a great impact on quantum information science. It has also led to the development of alternative theories to standard quantum theory and to new experimental tests (all so far confirming standard quantum theory). This course provides an introduction to modern research on quantum foundations. The course highlights theorems that illuminate the physical implications of quantum theory and some of its applications to quantum information science.
Material to be covered, time permitting:
Introduction to the Feynman path integral.
Entanglement and the relationship of quantum theory to special relativity.
Bell's theorem and non-locality.
The no-signalling principle.
The Pusey-Barrett-Rudolph theorem (2012);
assessment of claims that the PBR theorem proves the reality of the quantum wave function.
Simple models of decoherence and measurement.
The quantum measurement or reality problem: path integral
and decoherence approaches.
Many-worlds quantum theory: pros and cons.
An example of an alternative theory: the Ghirardi-Rimini-Weber
dynamical collapse model.
Examples sheets and examples classes will complement the course.
Desirable Previous Knowledge
A good understanding of undergraduate level quantum theory is required. (The Cambridge 1B Quantum
Mechanics course is a good starting point.)
Optional Introductory Reading
1. Benjamin Schumacher and Michael Westmoreland, Quantum Processes Systems, and Information,
Cambridge University Press, Chapters 1-8. This is a good starting text
for reviewing the key features of quantum theory in the context of quantum information. Also
useful are Benjamin Schumacher’s lectures on Quantum Theory, video archived at http://pirsa.org/C10028/.
Optional reading to complement course material:
2. John Bell, “Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, 2nd
edition, Chapters 1,2 and 22.
3. Robert Spekkens, lectures on Foundations of Quantum Mechanics given to Perimeter Scholars International
(2009). Video archived at pirsa.org, beginning with the first lecture at http://pirsa.org/09110168/
Very optional reading
For those interested in modern approaches to many-worlds quantum theory
and their problems. Note that this goes beyond the course material.
I do not recommend tackling these chapters until you are
sure you have mastered all the course material. (They could
make for interesting summer reading after the exams.)
4. “Many Worlds? Everett, Quantum Theory, and Reality", Simon Saunders, Jonathan Barrett, Adrian
Kent and David Wallace (eds.) (Oxford University Press, 2010), Chapter 8 (available at arXiv:0906.2718)
and Chapter 10 (available at arXiv:0905.0624).
There will be two examples classes, on dates to be arranged.