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

### Contacting me

My email address is wm266@cam.ac.uk, and I will be available in my office
(Pavilion F 0.14) every Monday 13:00 - 15:00.
### Examples classes

Felix Leditzky will run the
examples classes. There will be four examples classes:
1. 30th Oct, 2pm MR14. Example sheet 1 (19th Oct 2015)
2. 13th Nov, 2pm MR14. Example sheet 2 (2nd Nov 2015)
3. 27th Nov, 2pm MR14. Example sheet 3 (15th Nov 2015)
4. 29th Jan, 2pm MR14. Example sheet 4 (26th Dec 2015)

I will post the examples sheets here and hand them out in the lectures.

### 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

On the left is the date of lecture when it was handed out.
On the right is when latest version was uploaded.
Reports of errors and requests for clarification gratefully received at wm266@cam.ac.uk.
"v1.0" means the version handed out in the lecture Minor version increments mean
that errors have been corrected or explanation added (the changes are mentioned below).

I may put some handouts up in advance, but do remember that they
won't necessarily contain everything that's in the lecture.
On the other hand, they may contain things that aren't in the lectures,
so please do read them.

### 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.
### Errata

In handout 1 v1.0, in the defining equation for the inner product on
a tensor product space, "x" and "v" were the wrong way round. Corrected
in v1.1.
In the third lecture, in the definition of Bob's measurement for the
quantum strategy, I wrote (y-s/t) on the board when I should have written (s/t - y),
but the handout was correct.
In handout 3 v1.0, the last expression in section 5.1 was mangled,
and the footnote on page 3 was incomplete. Fixed in v1.1.
In handout 3, proposition 4, item 2: On the right hand side of the
equation the trace should have been acting on L_R, not on K_Q! Fixed in v1.2.
In handout 4, proof of proposition 12, the equation defining U_{AB}:
the lower limits on the sums over j and k were the wrong way round.
Fixed in v1.1.
In handout 6, section 8.3.1: The sign of the matrix given for Delta was incorrect,
and this error propagated to equation (8.10). This is corrected in v1.1.
The changes in v1.1 of handout 10 clarify various points which we discussed in the lecture.
v1.1 of handout 11 fixes numerous typos, and elaborates on the quantum source coding scenario.
In handout 12, first paragraph of 15.4, the definitions of E(0) and E(1) were
swapped, ie it should be that E(0) = T. This is fixed in v1.1.
In handout 12, there was a repeated error in the proof of Strong Subadditivity (Thm 21):
rho_{AB} ox rho_{C} should have been rho_{A} ox rho_{BC}. This is fixed in v1.1.