Good afternoon,
First of all, happy new year to all of you, I wish you joy and luck and success!
This year's first seminar talk will be given by Corsin Pfister:
Tuesday, Jan. 18, 17:00 in HIT J 52 (or maybe one of the K rooms, if available) on Hoenggerberg.
Best regards, Stefan
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Title: Tsirelson's bound in time
Abstract: The mathematical descriptions of joint probability distributions of measure- ment outcomes occurring in quantum mechanics are very different. Two local measurements on different subsystems are described by observables of tensor product form on a common tensor Hilbert space (two-systems correlations). Two measurements on the same system with an intermediate dynamical evolu- tion are described by a state update rule, trace-preserving completely positive maps and observables without a tensor product form (two-times correlations). Two-systems correlations are restricted by Tsirelson’s bound. One might ask if Tsirelson’s bound can also be used to find restrictions on two-times correlations. This thesis partially answers this question. Tsirelson’s bound is combined with an extended version of the Choi-Jamiolkowski Isomorphism, the Leifer Isomorphism, which shows an equivalence between two-systems and two-times correlations. It is shown that Tsirelson’s bound, together with the Leifer Iso- morphism, implies a tight bound on the average success probability of a special type of (2, 1,p)-Random Access Codings (RACs). RACs can be realised using two-systems correlations as well as two-times correlations, which allows a com- parison of the two cases. An attempt to interpret the analogue of the locality condition in the case of two-times correlations is made. It is found that two- times correlations used to realise this special type of (2, 1,p)-RAC cannot be used to communicate, as is the case for two-systems correlations.
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