Term: Spring 2025
Instructor: Girish Kulkarni
Venue and timings for lectures: Mondays, Tuesdays 4 PM - 5 PM, Fridays 5 PM - 6 PM
Office hours: Thursdays 4 - 6 PM
Course prerequisites: Quantum Mechanics - I
Course objective: To present a comprehensive introduction to foundational questions in quantum theory
Evaluation policy: 20% Assignments + 10% quizzes + 30% Mid-term exam + 40% end-term exam
Tentative list of topics to be covered:
Module 1: Overview of quantum theory (4 lectures)
Historical development of quantum theory, introduction to the postulates, juxtaposition between classical physics and quantum physics, states and ensembles, density matrices, distinction between coherent superpositions and incoherent mixtures, concept of purity or intrinsic coherence, Bloch sphere representation of qubits
Module 2: Quantum dynamics (4 lectures)
Composite systems and reduced density matrices, projective measurements, positive operator valued measures (POVMs), quantum state tomography with mutually unbiased bases (MUBs) and symmetric informationally-complete POVMs (SIC-POVMs), Neumark’s theorem, time evolution of quantum states, unitary maps,completely positive trace-preserving (CPTP) maps, unital maps, Stinespring dilation theorem
Module 3: Interpretation of the quantum state (4 lectures)
Young’s double slit interference, physical meaning of superpositions, ontic vs epistemic interpretation of the wavefunction, does it encode statistics of many identical systems or does it encode physical reality of individual quantum systems, Pusey-Barrett-Rudolph theorem,
Module 4: Measurement problem and decoherence (6 lectures)
Measurement problem, von-Neumann’s scheme, Schrodinger cat paradox, open quantum systems, decoherence and the quantum-to-classical transition, environment-induced superselection, decoherence-free subspaces, weak measurements and weak values, quantum Zeno effect
Module 5: Quantum nonlocality (6 lectures)
Locality, realism/ontology, Einstein-Podolsky-Rosen (EPR) argument, Bohr’s response, subsequent debates, Bell’s theorem, CHSH inequality, and the various loopholes, Nick Herbert’s FLASH proposal and subsequent discovery of the no-cloning theorem, GHZ inequality, temporal nonlocality, retrocausality, superdeterminism, quantum contextuality, Bell-Kochen-Specker theorem
Module 6: Quantum entanglement (6 lectures)
Entangled and separable states, relationship between global entanglement and local coherence, von Neumann entropy, Schmidt decomposition, entanglement measures in discrete and continuous variable systems, entanglement monogamy, local operations and classical communication (LOCC), transformations between entangled states and Nielsen’s majorization relations, Peres-Horodecki separability criterion
Module 7: Path integral picture of quantum mechanics (4 lectures)
Feynman’s path integral picture, Young’s double slit interference, complementarity, relationship between which-path information and interference visibility, propagators, solving example quantum problems in the path integral picture
Module 8: Alternative theories (4 lectures)
Bohmian mechanics, Everett’s theory and its implications, spontaneous wavefunction collapse models, stochastic electrodynamics, successes and limitations of these alternative theories
Module 9: Miscellaneous experiments (4 lectures)
Quantum eraser experiments, Wheeler’s delayed choice experiment, Hardy’s paradox, generation of entangled photons from parametric down-conversion, quantum teleportation, entanglement swapping, Wigner’s friend, violations of Bell’s inequalities, interaction-free measurements, ghost-imaging, imaging with undetected photons, macroscopic quantum interference experiments
Textbooks and reference material: