8.372 / 18.S996 - Quantum Information Science 3 8.372 / 18.S996 - Quantum Information Science 3
Instructor: Aram W
Harrow
Office hours: Tu 4-5 and Th 11-12, Room 6-416A
TA: Annie Wei
Office hours: Fri 10-11, Room 8-320
This is a third class in the MIT QIS sequence, following 8.370 and 8.371. It ran before in Fall 2020 as 8.S372/18.S996.
Psets and lecture notes will be made public. Registered students (including listeners) can access the canvas site and Piazza discussion boards. Any content only for registered students (such as pset solutions) will be labeled by the 
icon.
This is a third course in quantum information and computing theory, focused on special topics that may change from year to year. This year the focus is on quantum information theory, both understanding the core theory of the field, as well as application to physics.
The first part of the course will introduce the main questions and tools of quantum information theory, such as entropies, capacities, hypothesis testing, decoupling, random states and unitaries, symmetry, and entanglement. The second part will apply these tools, along with those from quantum complexity theory and error correction, to questions in many-body physics.
Click on the due date to upload your completed homework.
| Assignment | Due Date | Solutions | Topic |
|---|---|---|---|
| Problem set 1 | Fri, Sep 16 | |
trace distance and bit commitment |
| Problem set 2 | Fri, Sep 23 |
|
channels and types |
| Problem set 3 | Fri, Sep 30 | |
gentle measurement, channel fidelity, entropy inequalities |
| Problem set 4 | Fri, Oct 7 | |
Gibbs distributions and compression with side information |
| Problem set 5 | Fri, Oct 14 |
| data compression converse |
| Problem set 6 | Fri, Oct 21 | |
classical and entanglement-assisted channel capacities |
| Problem set 7 | Fri, Oct 28 | unital channels and additivity | |
| Problem set 8 | Fri, Nov 4 | data hiding with Werner states | |
| Project proposal | Fri, Nov 18 | ||
| Problem set 9 | Fri, Dec 2 | distillation, monogamy and symmetry | |
| Project Presentation | Tues, Dec 13, 9am | 3 min for individuals, 5 min for groups | |
| Project paper | Wed, Dec 14 |
Sep 8, 2022: Introduction, bit commitment
Review material: 8.371 lectures on density
matrices, quantum
operations
Related reading: Chap 5 of [Wilde].
Sep 13, 2022: purifications and the "no bit commitment" theorem
Related reading: early review of the bit-commitment no-go paper.
Sep 15, 2022: trace distance and fidelity
Review materials: Chap 9 of [Wilde], Section 3.2 of [Wat].
Sep 20, 2022: classical information theory: entropy and compression
Review material: Chap 10 of [Wilde]
Related reading: C. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, 1948. Shannon, The Bandwagon, IRE Transactions on Information Theory, 1956.
Sep 22, 2022: quantum entropy and compression.
Review material: Chap 11 of [Wilde]
Related reading: algorithmic cooling on wikipedia.
Sep 27, 2022: relative entropy and entropy inequalities
Review material: Chaps 10 and 11 of [Wilde]
Sep 29, 2022: quantum relative entropy
Related reading: Igor Bjelakovic, Rainer Siegmund-Schultze, Quantum Stein's lemma revisited, inequalities for quantum entropies, and a concavity theorem of Lieb, quant-ph/0307170, 2012.
Oct 4, 2022: hypothesis testing
Oct 6, 2022: noisy channel coding
Review material: Chap 2 of [Wilde]
Oct 13, 2022: examples and achievability proof of the channel capacity
Related reading: Tomohiro Ogawa, Hiroshi Nagaoka; A New Proof of the Channel Coding Theorem via Hypothesis Testing in Quantum Information Theory. arXiv:quant-ph/0208139, IEEE Trans. Inf. Th. 2002.
Pranab Sen, Achieving the Han-Kobayashi inner bound for the quantum interference channel by sequential decoding. arXiv:1109.0802, IEEE Symp. on Inf. Th. 2012.
Oct 18, 2022: Fannes's inequality. Converse to capacity theorem for classical and quantum channels.
Review material: Chapters 16 and 20 of [Wilde]
Related reading: Andreas Winter. Coding Theorem and Strong Converse for Quantum Channels. 1409.2536. IEEE Trans. Inf. Th. 1999. Andeas Winter. Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints. 1507.07775. Commun. Math. Phys 2016.
Oct 20, 2022: Applications of HSW to tomography and random access codes.
Review material: Jeongwan Haah, Aram W. Harrow, Zhengfeng Ji, Xiaodi Wu, Nengkun Yu. Sample-optimal tomography of quantum states. 1508.01797. STOC 2016 and IEEE Trans. Inf. Th. 2017.
Scott Aaronson. The Learnability of Quantum States.
quant-ph/0608142. Proc. Roc. Soc. A. 2007.
Ashwin Nayak. Optimal lower bounds for quantum automata and random access codes. quant-ph/9904093. FOCS 1999.
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