Reading group on entanglement and cryptography

MIT, Spring 2013

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Wednesdays 4-6pm, G531. See here for an introductory blog post, and here for a partial bibliography of suggested readings. Schedule:

April 3rd. Thomas will give a general introduction to device independence, and we will discuss which direction to take the reading group in. See this post for a brief introduction.
April 10th. Matt talked about the CHSH game, optimal strategies and rigidity. Shelby wrote up a brief summary and some notes: here and here. Related preparatory readings include Section 3.1 in CHTW and (for the more courageous) Section 4 in RUV. For a historical perspective I also recommend taking a look at Bell's original 1964 paper On the Einstein-Podolsky-Rosen paradox.
April 17th. Mohammad gave an introduction to non-signaling distributions and monogamy. He presented Ekert's protocol for QKD, as well as the BHK paper on basing security of quantum key distribution solely on the no-signaling principle. Kristan wrote up some notes; see also here for the missing proof of monogamy of the PR box.
April 24th. Han-Hsuan told us about monogamy of entanglement and non-signaling distributions in the context of games. See this paper by Ben Toner, this one by Toner and Verstraete, and this more recent survey by Seevinck. Felipe wrote some notes (here, here and here) for the lecture.
May 1st. Henry introduced us to conditional entropy measures of quantum information (von Neuman, min- and max-) and derived an entropic uncertainty relation with quantum side information due to Berta et al. He also showed how that relation could be used to prove device-independent security of an interesting scheme for QKD due to Lim et al. Good additional resources on the topic of entropy measures and quantum key distribution are Renato Renner's Ph.D. thesis and the recent book by Mark Wilde on quantum information theory.
May 9th (Note the unusual day/time/location: Thursday, 4pm, G431). Felipe told us about measurement-based quantum computation and blind quantum computing. A good introduction to measurement-based computation by Browne and Briegel can be found here. See the original paper on blind quantum computing by Broadbent et al., and follow-up work by Fitzimons and Kashefi.
May 13th (Monday, 10am, G631) Juan will present the paper by Colbeck and Renner on free randomness amplification. See also follow-up work by Gallego et al. and also this paper by Thinh et al. For a more leisurely introduction to the problem of randomness manipulation using games/Bell inequalities, see Chapter 5 in Colbeck's PhD. thesis.
May 20th (noon) Dimiter will talk about rigidity of strategies for the CHSH game and applications to the problem of testing quantum mechanics. We will see the proof of rigidity by McKague et al. See also the RUV paper for further developments on that topic.

A few "foundational" papers (nice bedtime reading!):

Bell's 1964 paper: On the Einstein-Podolsky-Rosen paradox (and while we're at it, the EPR paper itself: Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?).
Ekert's paper on QKD: Quantum cryptography based on Bell's theorem.
Terhal's "speach" on monogamy: Is entanglement monogamous?
The Popescu-Rohrlich PR box: Nonlocality as an axiom for quantum theory. See also their very nice The joy of entanglement, a good introduction to entanglement as a resource.
Roger Colbeck's Ph.D. thesis gives a good introduction to the problem of realizing various primitives in two-party cryptography under different types of physical assumptions.

Some initial topics we might explore:

Classical testing of a quantum computer: the paper by Reichardt, Unger and Vazirani will likely be among the first we will read: get started early!
Device-independent key distribution : see this paper by Barrett, Colbeck and Kent for a proposal based on no-signaling only, and this one for a more efficient proposal whose proof of security uses quantum mechanics.
Randomness certification: an initial proposal by Pironio et al., and follow-up work by Gelles, Fehr and Schaffner. See also this paper by Colbeck and Renner for a related task of "free randomness amplification" (and follow-up work).
Blind quantum computing: a proposal by Aharonov et al., and another by Broadbent et al. (see also here for reports of an experimental implementation!).
de Finetti-type theorems. See this paper by Brandao and Harrow for a very recent result that could be applicable in the context of device-independent cryptography.