This course will cover the basics of Quantum Foundations under three main headings. Part I – Novel effects in Quantum Theory. A number of interesting quantum effects will be considered. (a) Interferometers: Mach-Zehnder interferometer, Elitzur-Vaidman bomb tester, (b) The quantum-Zeno effect. (c) The no cloning theorem. (d) Quantum optics (single mode). Hong-Ou-Mandel dip. Part II Conceptual and interpretational issues. (a) Axioms for quantum theory for pure states. (b) Von-Neumann measurement model. * (c) The measurement (or reality) problem. (d) EPR Einstein’s 1927 remarks, the Einstein-Podolsky-Rosen argument. (e) Bell’s theorem, nonlocality without inequalities. The Tirolson bound. (f) The Kochen-Specker theorem and related work by Spekkens (g) On the reality of the wavefunction: Epistemic versus ontic interpretations of the wavefunction and the Pusey-Barrett-Rudolph theorem proving the reality of the wave function. (h) Gleason’s theorem. (i) Interpretations. The landscape of interpretations of quantum theory (the Harrigen Spekkens classification). The de Broglie-Bohm interpretation, the many worlds interpretation, wave-function collapse models, the Copenhagen interpretation, and QBism. Part III Structural issues. (a) Reformulating quantum theory: I will look at some reformulations of quantum theory and consider the light they throw on the structure of quantum theory. These may include time symmetric quantum theory and weak measurements (Aharonov et al), quantum Bayesian networks, and the operator tensor formalism. (b) Generalised probability theories: These are more general frameworks for probabilistic theories which admit classical and quantum as special cases. (c) Reasonable principles for quantum theory: I will review some of the recent work on reconstructing quantum theory from simple principles. (d) Indefinite causal structure and indefinite causal order. Finally I will conclude by looking at (i) the close link between quantum foundations and quantum information and (ii) possible future directions in quantum gravity motivated by ideas from quantum foundations.
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