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Analysis and Probability Seminar- October 18, 2016

Posted on October 7, 2016

Tuesday, October 18, 2016 (3:00 p.m. in Yost 306)

Title: Can one achieve truly quantum correlations with PPT states? (Part III)

Speaker: Ben Li (PhD Student, Case Western Reserve University)

Abstract: If (X_i) and (Y_j) are two sequences of random variables, we call [E(X_iY_j)] their correlation matrix (this is closely related to the covariance matrix from probability). In this talk, we will consider quantum analogues of correlation matrices, which correspond to bipartite quantum systems, where each of the parties has the choice of a number of dichotomic observables. Some quantum correlation matrices can not be achieved with classical variables, this is an example of a violation of a certain “Bell inequality.” An explicit upper bound – due to Tsirelson and related to the Grothendieck inequality from functional analysis – on such violations will be given. In particular, for 2 x 2 and 3 x 3 matrices, no violation is possible if the quantum correlation matrix is induced by a state with positive partial transpose (PPT state). The main content of this talk follows from the work of R.F. Werner and M.M. Wolf.

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