## Notes for the Part III Quantum Information Theory course (Michaelmas 2015-2016)

### Handouts

All the handouts in one file (27th Dec 2015).
9th Oct 2015: Handout 1 v1.1 (16th Oct 2015). Mathematical background; Postulates of Quantum Mechanics
12th Oct 2015: Handout 2 v1.0 (12th Oct 2015). CHSH game
16th Oct 2015: Handout 3 v1.2 (19th Oct 2015). More on CHSH; Density operators; Purifications
19th Oct 2015: Handout 4 v1.1 (23th Oct 2015). Time evolution; Operations
23th Oct 2015: Handout 5 v1.0 (23th Oct 2015). Instruments; POVMs
28th Oct 2015: Handout 6 v1.1 (28th Oct 2015). State discrimination; Holevo-Helstrom theorem; Unambiguous state discrimination
30th Oct 2015: Handout 7 v1.0 (30th Oct 2015). Entanglement; Schmidt-decomposition; Mixed-state entanglement; PPT states
4th Oct 2015: Handout 8 v1.0 (4th Nov 2015). Dense coding; Teleportation
9th Nov 2015: Handout 8b v1.0 (6th Nov 2015). Comments on teleportation; Cloning and superluminal communication
6th Nov 2015: Handout 9 v1.1 (6th Nov 2015). Fidelity; Fidelity of operations
11th Nov 2015: Handout 10 v1.1 (11th Nov 2015). Data compression 1: Classical and quantum data compression
16th Nov 2015: Handout 11 v1.1 (16th Nov 2015). Data compression 2: Classical and quantum source coding theorems
18th Nov 2015: Handout 12 v1.1 (24th Nov 2015). Quantum and classical entropies; hypothesis testing; data processing inequalities; Fano's inequality
25th Nov 2015: Handout 13 v1.0 (25th Nov 2015). Channel coding 1: Memoryless quantum channels; Capacity; Holevo bound; Holevo information; HSW theorem and proof of converse
2nd Dec 2015: Handout 14 v1.0 (16th Dec 2015). Channel coding 2: Achievability part of HSW theorem

### Other resources

On classical information theory:
D. J. C. MacKay,
"Information Theory, Inference, and Learning Algorithms".
C. E. Shannon,
"A Mathematical Theory of Communication",
Bell System Technical Journal 27 (3): 379-423 (1948).

On quantum information theory:
M. M. Wilde,
"From Classical to Quantum Shannon Theory".

### Acknowledgements

The handouts draw on a number of sources: Nilanjana Datta's handouts for the course from previous years;
the texts of MacKay, Cziszár and Körner, Nielsen and Chuang, and Wilde;
The lecture notes for John Watrous's quantum information course.