# Foundations of Quantum Theory: Non-Relativistic Approach

- Institution: IISER Mohali
- Department: Physics
- Teacher: Prof. Sandeep Kumar Goyal
- Level: Graduate
- Language: English
- Subjects: Physics
- Source: [NPTEL](https://nptel.ac.in/courses/115106536)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/115106536)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Quantum theory (QT) is empirically a very successful theory; there is however an apparent lack of understanding of the theory. This is mostly due to the fact that, unlike the space-time structure, the cut between the ontology and epistemology in QT is difficult to resolve. The two fundamental concepts–the non-local correlations (entanglement) between space-like separated systems and the indistinguishability (non-orthogonality) of quantum states–is widely believed to separate QT from classical theories. In this course we take a foundational approach to QT from the outside: i.e., since classical theories are completely devoid of entanglement, it is compared with various foil theories that are also non-local and indistinguishable in the sense of QT, such that their special nature in the theory can be quantified. The two concepts will be explained in this course through variety of topics it has motivated in the field of quantum information and computation, both in non relativistic settings. In the followup course proposed, we will also discuss the relativisitic approach to foundations of quantum theory.

Intended audience: Msc 1st and 2nd year, PhD students

Prerequisites: BSc in Physics and a good grasp of quantum physics

## Lectures

1. [Axiomatic Approach to Quantum Mechanics - Part 01](https://invisiblenetwork.ai/learn/nptel/115106536/3d0155c9dc07) (YouTube)
2. [Axiomatic Approach to Quantum Mechanics - Part 02](https://invisiblenetwork.ai/learn/nptel/115106536/f064dcd67262) (YouTube)
3. [Linear Vector Space](https://invisiblenetwork.ai/learn/nptel/115106536/415f2187ba63) (YouTube)
4. [Linear Operators - Part 01](https://invisiblenetwork.ai/learn/nptel/115106536/fb9546a79db0) (YouTube)
5. [Linear Operators - Part 02](https://invisiblenetwork.ai/learn/nptel/115106536/eb16eef3f6f1) (YouTube)
6. [Qubits: Introduction](https://invisiblenetwork.ai/learn/nptel/115106536/f3a4dca75f4d) (YouTube)
7. [Qubits: State Tomography](https://invisiblenetwork.ai/learn/nptel/115106536/f5a44e9bf4a3) (YouTube)
8. [Qubits: Density Operators - Part 01](https://invisiblenetwork.ai/learn/nptel/115106536/ba33becd4fee) (YouTube)
9. [Qubits: Density Operators - Part 02](https://invisiblenetwork.ai/learn/nptel/115106536/044a91043c70) (YouTube)
10. [Qubits: Unitary Transformation](https://invisiblenetwork.ai/learn/nptel/115106536/0e52005676c3) (YouTube)
11. [Qubits: Bloch Sphere](https://invisiblenetwork.ai/learn/nptel/115106536/ada3b36804fe) (YouTube)
12. [Composite Systems: Pure States, Schmidt Decomposition, Operators Acting on Composite Systems - Part 01](https://invisiblenetwork.ai/learn/nptel/115106536/2de7fac76053) (YouTube)
13. [Composite Systems: Pure States, Schmidt Decomposition, Operators Acting on Composite Systems - Part 02](https://invisiblenetwork.ai/learn/nptel/115106536/13ac9c2956de) (YouTube)
14. [Composite Systems: Density Operators](https://invisiblenetwork.ai/learn/nptel/115106536/e24cb566101a) (YouTube)
15. [Quantum Maps: Positive Maps](https://invisiblenetwork.ai/learn/nptel/115106536/56cd3506ae36) (YouTube)
16. [Quantum Maps: Completely Positive Maps - Part 01](https://invisiblenetwork.ai/learn/nptel/115106536/b1f0a4de6e9e) (YouTube)
17. [Quantum Maps: Completely Positive Maps - Part 02](https://invisiblenetwork.ai/learn/nptel/115106536/b033ac03aeba) (YouTube)
18. [Measurements: Introduction](https://invisiblenetwork.ai/learn/nptel/115106536/00f470acfb99) (YouTube)
19. [Measurements: POVM](https://invisiblenetwork.ai/learn/nptel/115106536/d2b3f4b3c005) (YouTube)
20. [Measurement: Optical Scheme for POVM](https://invisiblenetwork.ai/learn/nptel/115106536/0a703f2d93cd) (YouTube)
21. [Measurements: State Discrimination](https://invisiblenetwork.ai/learn/nptel/115106536/494235a342be) (YouTube)
22. [Measurements: Weak Measurements](https://invisiblenetwork.ai/learn/nptel/115106536/a061eccbc84a) (YouTube)
23. [Entanglement: Introduction](https://invisiblenetwork.ai/learn/nptel/115106536/f3eca292d9b1) (YouTube)
24. [Entanglement Measures](https://invisiblenetwork.ai/learn/nptel/115106536/32d0d58efadc) (YouTube)
25. [EPR Paradox and Bohr’s Argument, Bohm’s Argument and Mermin’s Argument - Part 01](https://invisiblenetwork.ai/learn/nptel/115106536/94996cd337d3) (YouTube)
26. [EPR Paradox and Bohr’s Argument, Bohm’s Argument and Mermin’s Argument - Part 02](https://invisiblenetwork.ai/learn/nptel/115106536/782aa28c6403) (YouTube)
27. [Hidden Variable Theory, Bell model, Bell Inequality, Bell CHSH Inequality](https://invisiblenetwork.ai/learn/nptel/115106536/ee11d9e46d3d) (YouTube)
28. [Open Quantum Systems: Introduction - Part 01](https://invisiblenetwork.ai/learn/nptel/115106536/e936b7c64170) (YouTube)
29. [Open Quantum Systems: Introduction - Part 02](https://invisiblenetwork.ai/learn/nptel/115106536/abca1e493eb2) (YouTube)
30. [Open Quantum Systems: Introduction - Part 03](https://invisiblenetwork.ai/learn/nptel/115106536/a7e2f7c06326) (YouTube)
31. [Open Quantum Systems: Optical Master Equation, Thermalization](https://invisiblenetwork.ai/learn/nptel/115106536/747ad96d5dcf) (YouTube)
32. [Open Quantum Systems: Solving Master Equaitons](https://invisiblenetwork.ai/learn/nptel/115106536/9eaee4f6f664) (YouTube)
33. [Open Quantum Systems: Quantum Trajectory Aproach](https://invisiblenetwork.ai/learn/nptel/115106536/00c1853a2794) (YouTube)
34. [Open Quanutm Systems: Decoherence](https://invisiblenetwork.ai/learn/nptel/115106536/0f20a92e388f) (YouTube)