8.S372/18.S996 Quantum Information Science 3

Fall 2020

Lecture: TR1-2:30 zoom link for registered students

Instructor: Aram W Harrow
Office hours: TR 2:30-3:30

TA: Michael DeMarco
Office hours: F 10:30-11:30

Psets and lecture notes will be made public. Pset solutions, Piazza discussion boards and real-time videos will be only for registered class participants (including registered listeners) and will be marked by the icon.

Assignments

Problem set 1. Due Fri, Sep 11. upload answers , solutions ,
Problem set 2. Due Fri, Sep 18. upload answers , solutions ,
Problem set 3. Due Fri, Sep 25. upload answers , solutions
Problem set 4. Due Fri, Oct 2. upload answers , solutions
Problem set 5. Due Fri, Oct 9. upload answers , solutions
Problem set 6. Due Fri, Oct 16. upload answers , solutions
Problem set 7. Due Fri, Oct 23. upload answers , solutions
Problem set 8. Due Fri, Nov 13. upload answers , solutions
Problem set 9. Due Fri, Dec 4. upload answers , solutions
Final project. Proposal due Nov 6; presentations tentatively Dec 1, 3, 8; paper due Dec 8.
Other relevant dates. Oct 2 is add date and Nov 18 is drop date. MIT academic calendar

Lectures

All lecture notes in one file

Sep 1, 2020: Introduction, purification (txt, pdf, video )
Review material: 8.371 lectures on density matrices, quantum operations
Related reading: Chap 5 of [Wilde].
Sep 3, 2020: purification uniqueness, cryptography and bit commitment (txt, pdf, video )
Related reading: early review of the bit-commitment no-go paper.
Sep 8, 2020: norms, trace distance, fidelity, Uhlmann's theorem (tablet notes, pdf, video )
Review materials: Chap 9 of [Wilde], Section 3.2 of [Wat].
Sep 10, 2020: classical information theory: entropy and compression (tablet notes, pdf, video )
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 15, 2020: quantum entropy and compression. (tablet notes, pdf, video )
Review material: Chap 11 of [Wilde]
Related reading: algorithmic cooling on wikipedia.
Sep 17, 2020: relative entropy (notes, pdf, video )
Review material: Chaps 10 and 11 of [Wilde]
Sep 22, 2020: noisy channel coding (tablet notes, pdf, video )
Review material: Chap 2 of [Wilde]
Sep 24, 2020: channel coding: converse and quantum coding (HSW) (tablet notes, pdf, video )
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
Sep 29, 2020: packing lemma and completing the proof of HSW (tablet notes, pdf, video )
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 1, 2020: quantum relative entropy (tablet notes, pdf, video )
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 6, 2020: Applications of relative entropy. (tablet notes, pdf, video )
Related reading: Jess Riedel, The interpretation of free energy as bit-erasure capacity. Fernando G.S.L. Brandao, Martin B. Plenio; Entanglement Theory and the Second Law of Thermodynamics, arXiv:0810.2319; Nature Physics 4, 873 (2008). Fernando G. S. L. Brandão, Michał Horodecki, Jonathan Oppenheim, Joseph M. Renes, Robert W. Spekkens; The Resource Theory of Quantum States Out of Thermal Equilibrium; arXiv:1111.3882, Phys. Rev. Lett. 111, 250404 (2013).
Oct 8, 2020: Classical capacity. Entangled channel inputs. Diamond norm and channel simulation. (tablet notes, pdf, video )
Related reading: Michael Horodecki, Peter W. Shor, Mary Beth Ruskai. General Entanglement Breaking Channels. arXiv:quant-ph/0302031, Rev. Math. Phys 15, 629--641 (2003). Charles H. Bennett, Patrick Hayden, Debbie W. Leung, Peter W. Shor, Andreas Winter. Remote preparation of quantum states. arXiv:quant-ph/0307100, IEEE Trans. Inf. Th. 2005.
Oct 15, 2020: Entanglement-assisted and quantum capacity(tablet notes, pdf, video )
Review material: Chapter 21 of [Wilde]
Related reading: Charles H. Bennett, Peter W. Shor, John A. Smolin, Ashish V. Thapliyal. arXiv:quant-ph/0106052. IEEE Trans. Inf. Th. 2002. A. S. Holevo. On entanglement-assisted classical capacity. arXiv:quant-ph/0106075. J. Math. Phys. 2002 Graeme Smith. Quantum Channel Capacities. arXiv:1007.2855. Dennis Kretschmann, Reinhard F Werner. Tema Con Variazioni: Quantum Channel Capacity. arXiv:quant-ph/0311037
Oct 20, 2020: Quantum capacity, coherent information, PPT, superactivation (tablet notes, pdf, video )
Related reading: Graeme Smith, Jon Yard. Quantum Communication With Zero-Capacity Channels. arXiv:0807.4935, Science 2008. perspective on this: Jonathan Oppenheim. For quantum information, two wrongs can make a right. arXiv:1004.0052. Science 2008
Oct 22, 2020: Cobits and proof of the quantum capacity theorem (tablet notes, pdf, video )
Review material: Chapters 6, 7 and 22 of [Wilde]
Related reading: I. Turner. Scientist knows less than nothing, Bristol Evening Post, Aug 5, 2005. I. Devetak, A. W. Harrow, A. Winter. A family of quantum protocols. arXiv:quant-ph/0308044, PRL 2004. A. W. Harrow. Coherent Communication of Classical Messages. arXiv:quant-ph/0307091, PRL 2004. Karol Horodecki, Michal Horodecki, Pawel Horodecki, Jonathan Oppenheim. General paradigm for distilling classical key from quantum states. arXiv:quant-ph/0506189, IEEE Trans. Inf. Th. 2009 Informal version: Michal Horodecki, Jonathan Oppenheim, Andreas Winter. Quantum information can be negative. arXiv:quant-ph/0505062 Nature 2005. Formal verison: Michal Horodecki, Jonathan Oppenheim, Andreas Winter. Quantum state merging and negative information. arXiv:quant-ph/0512247. Comm. Math. Phys. 2007. Anura Abeyesinghe, Igor Devetak, Patrick Hayden, Andreas Winter. The mother of all protocols: Restructuring quantum information's family tree. arXiv:quant-ph/0606225, Proc. R. Soc. A. 2009
Oct 27, 2020: Random states and entanglement (tablet notes, pdf video )
Review material: A. W. Harrow, The Church of the Symmetric Subspace, arXiv:1308.6595
Related reading: Patrick Hayden, Debbie W. Leung, Andreas Winter. Aspects of generic entanglement. arXiv:quant-ph/0407049. Comm. Math. Phys 2006
Oct 29, 2020: Random matrices and randomizing maps(tablet notes, pdf, video )
Nov 3, 2020: Representation theory, Schur-Weyl duality, and random states (tablet notes, pdf, video )
Review material: Chapter 5 of the dissertation of A. W. Harrow [quant-ph/0512255], Chapter 1 of the dissertation of M. Christandl quant-ph/0604183.
Related reading: Roe Goodman, Nolan R. Wallach. Symmetry, Representations, and Invariants, Graduate Texts in Mathematics vol 255, 2009. (pdf available using MIT libraries)
Nov 5, 2020: merging and FQSW (tablet notes, pdf, video )
Related reading: I. Devetak. A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal. quant-ph/0505138.
Nov 10, 2020: Black holes as mirrors, quantum capacity from decoupling, and k-designs (tablet notes, pdf, video )
Related reading: Patrick Hayden, John Preskill. Black holes as mirrors: quantum information in random subsystems. arXiv:0708.4025 Don N. Page. Information in Black Hole Radiation. hep-th/9306083. Joel Tropp. User-friendly tail bounds for sums of random matrices. 1004.4389. Daniel Harlow. Jerusalem Lectures on Black Holes and Quantum Information. 1409.1231. Patrick Hayden, Michal Horodecki, Andreas Winter, Jon Yard. A decoupling approach to the quantum capacity. quant-ph/0702005
Nov 12, 2020: Random circuits and k-designs (tablet notes, pdf, video )
Related reading: Fernando G. S. L. Brandao, Aram W. Harrow, Michal Horodecki. Local random quantum circuits are approximate polynomial-designs. 1208.0692, CMP 2016. Nicholas Hunter-Jones. Unitary designs from statistical mechanics in random quantum circuits. 1905.12053.
Nov 17, 2020: stat mech approach to k-designs, and intro to de Finetti theorems (tablet notes, pdf, video )
Related reading: P. Diaconis, D. Freedman. Finite Exchangeable Sequences. Annals of Probability 1980. Giulio Chiribella. On quantum estimation, quantum cloning and finite quantum de Finetti theorems. 1010.1875.
Nov 19, 2020: de Finetti theorems and monogamy of entanglement (tablet notes, pdf, video )
Related reading: Renato Renner. Symmetry implies independence. quant-ph/0703069, Nature 2007. Thomas Vidick, Henry Yuen. A simple proof of Renner's exponential de Finetti theorem. 1608.04814. Aram Harrow, The Church of the Symmetric Subspace, 1308.6595. Cécilia Lancien, Andreas Winter. Flexible constrained de Finetti reductions and applications. 1605.09013, JMP 2017. Matthias Christandl, Andreas Winter. "Squashed Entanglement" - An Additive Entanglement Measure. quant-ph/0308088, JMP 2004.

References

[NC] Quantum Computation and Quantum Information, by Michael Nielsen and Isaac Chuang.
[KSV] Classical and Quantum Computation, by Kitaev, Shen and Vyalyi
8.370x video lectures, mostly by Peter Shor
John Preskill lecture notes
[Wilde] Quantum Information Theory (aka "From Classical to Quantum Shannon Theory.") by Mark Wilde. book and arxiv
[Wat] The Theory of Quantum Information by John Watrous.
Other recommended lecture notes: Umesh Vazirani (traditional and edx), Andrew Childs, Scott Aaronson, Ronald de Wolf