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
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    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.