Quantum Entanglement: Fundamentals, measures and applications

ABOUT THE COURSE :In recent times, there is huge interest in quantum computation and quantum information science. In this context, quantum entanglement is drawing tremendous interests from students as well as researchers. Unfortunately, the topic of entanglement is not covered anywhere in an accessible way. This course will enable the students to understand the fundamentals behind quantum entanglement. Also, they will learn associated mathematical tools to quantify entanglement. The course will prepare and motivate them to take a research carrier in this highly promising modern area of inter-disciplinary research.INTENDED AUDIENCE : Students from B.Tech. Engineering Physics, M.Sc. Physics and B.Tech. Electrical Engineering. Also, Ph.D. students working in the area of Condensed Matter Physics and Quantum Optics.PREREQUISITES : An elementary course on Quantum Mechanics

Week 1:Introduction; Review of quantum mechanics

1. Introduction
2. Postulates of Quantum Mechanics; Quantum mechanics of two-level systems
3. Density matrix formalism

Week 2:Physics of Quantum Entanglement

1. Bell’s inequalities and theorem; Einstein-Podolsky-Rosen gedanken experiment;
2. Schrödinger’s notion of “entanglement”; Bohm’s spin version of the EPR experiment
3. Schmidt decomposition and entanglement

Week 3:Measures of Quantum entanglement; continuous variable quantum systems, Gaussian states

1. Introduction to continuous variable quantum systems; quantum phase-space representation
2. Gaussian states
3. Logarithmic negativity as a measure

Week 4:Applications of Quantum Entanglement; Quantum teleportation, Super dense coding, optomechanical entanglement

1. Quantum teleportation; Super dense coding; quantum cryptography
2. Optomechanical entanglement-I
3. Optomechanical entanglement-II