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SUMMARY:Self-testing of binary observables based on commutation - Jed Kani
 ewski
DTSTART:20170323T141500Z
DTEND:20170323T151500Z
UID:TALK70786@talks.cam.ac.uk
CONTACT:Steve Brierley
DESCRIPTION:In this talk we consider the problem of certifying binary\nobs
 ervables based on a Bell inequality violation alone\, a task known as\nsel
 f-testing of measurements. We introduce a family of commutation-\nbased me
 asures\, which encode all the distinct arrangements of two\nprojective obs
 ervables on a qubit. These quantities by construction\ntake into account t
 he usual limitations of self-testing and since they\nare `weighted' by the
  (reduced) state\, they automatically deal with\nrank-deficient reduced de
 nsity matrices. We show that these measures\ncan be estimated from the obs
 erved Bell violation in several scenarios.\nThe trade-offs turn out to be 
 tight and\, in particular\, they give non-\ntrivial statements for arbitra
 rily small violations. On the other\nextreme\, observing the maximal viola
 tion allows us to deduce precisely\nthe form of the observables\, which im
 mediately leads to a complete\nrigidity statement. In particular\, we show
  that the n-partite Mermin-\nArdehali-Belinskii-Klyshko inequality self-te
 sts the n-partite\nGreenberger-Horne-Zeilinger state and maximally incompa
 tible qubit\nmeasurements on every site for all n. Our results imply that 
 any pair\nof projective observables on a qubit can be certified in a robus
 t\nmanner. Finally\, we show that commutation-based measures give a\nconve
 nient way of expressing relations between more than two\nobservables. This
  talk is based on https://arxiv.org/abs/1702.06845 .
LOCATION:MR5\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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