This advanced UG level elective course will cover basic themes in quantum entanglement, quantum information and open quantum systems. These foundational topics are essential for, and ubiquitous in, quantum condensed matter, high energy physics, quantum optics and quantum computing.

Brief Course Outline

Quantum Mechanics of Composite systems: Direct products, mixed states and density operators, partial trace, Schmidt decomposition. Qubits, Bloch sphere. Identical particles - symmetric and antisymmetric wave functions.

*Fock space.

Quantum Entanglement: Separable and entangled states. Einstein-Podolsky-Rosen experiment, Bell’s theorem, CHSH inequality, GHZ states, no-cloning theorem. Quantum entanglement measures. Quantum Channels and Completely Positive Trace Preserving maps, quantum entropy and information measures. Relative Entropy, mutual information, sub-additivity. Hidden variables, non-locality and Popescu-Rosen boxes.

*Multipartite entanglement

Time evolution, Lindbladt equation and open system dynamics. Simple qubit and quantum optics examples, dephasing and depolarizing channels.

*Decoherence, Caldeira-Legett model, thermalization in quantum systems.

Prerequisites

Thorough knowledge of Quantum Mechanics at 3000 level UG physics.

Resources

We will use relevant sections of the following textbook:

Quantum Processes, Systems and Information, by B. Schumacher and M. Westmoreland [Cambridge, CUP], together with

Entangled systems: New Directions in Quantum Physics, by J. Audretsch [Wiley-VCH], and John Preskill’s Caltech PH229 lecture notes.