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Flexible constrained de Finetti reductions and parallel repetition of multi-player non-local games

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Roughly speaking, de Finetti type theorems allow to reduce the analysis of permutation-invariant scenarios to that of i.i.d. ones. In this talk, I will present certain variants of such de Finetti reductions, and show how they can be used to study the parallel repetition of multi-player non-local games. More precisely, the problem one usually wants to solve in this context is the following: if players sharing certain physical resources cannot win one instance of a game with probability 1, does their probability of winning n instances of this game at the same time decays to 0 exponentially fast? Perhaps surprisingly, the answer to this question is not trivially “yes”, even though I will show that e.g. in the case of no-signalling correlations between the players, it is indeed “yes” in almost full generality. If time allows, I will also discuss how such de Finetti reductions can be used to study the (weakly) multiplicative behavior of other quantities showing up in quantum information theory. This talk will be based on joint work with Andreas Winter, either appearing in arXiv[quant-­‐ph]1506.07002 or arXiv[quant-­‐ph]1605.09013.

This talk is part of the CQIF Seminar series.

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