|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Self-testing of binary observables based on commutation
If you have a question about this talk, please contact Steve Brierley.
In this talk we consider the problem of certifying binary observables based on a Bell inequality violation alone, a task known as self-testing of measurements. We introduce a family of commutation- based measures, which encode all the distinct arrangements of two projective observables on a qubit. These quantities by construction take into account the usual limitations of self-testing and since they are `weighted’ by the (reduced) state, they automatically deal with rank-deficient reduced density matrices. We show that these measures can be estimated from the observed Bell violation in several scenarios. The trade-offs turn out to be tight and, in particular, they give non- trivial statements for arbitrarily small violations. On the other extreme, observing the maximal violation allows us to deduce precisely the form of the observables, which immediately leads to a complete rigidity statement. In particular, we show that the n-partite Mermin- Ardehali-Belinskii-Klyshko inequality self-tests the n-partite Greenberger-Horne-Zeilinger state and maximally incompatible qubit measurements on every site for all n. Our results imply that any pair of projective observables on a qubit can be certified in a robust manner. Finally, we show that commutation-based measures give a convenient way of expressing relations between more than two observables. This talk is based on https://arxiv.org/abs/1702.06845 .
This talk is part of the CQIF Seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsComputer Laboratory Programming Research Group Seminar JCBS Jesus College Biological Society Violence Research Center
Other talksMyelination in development and learning Tales from the Fen Edge: past environments. peat, marl and mud Nuclear norm methods for frequency domain system identification Free speech and seditious libel: James Gillray and the crisis of Revolution The 2-linearity of the free group and the topology of the punctured disc Easter Term Poster Session