ON-LINE QLunch: Mizanur Rahaman
Speaker: Mizanur Rahaman, Birla Institute of Technology and Science, Pilani, Goa Campus, India
Title: Bisynchronous Games and Positively Factorizable Maps
Abstract
In the theory of non-local games, the graph isomorphism game stands out to be a very intriguing one. Specially when the algebra of the game is considered. This is because this game establishes a close connection between the perfect winning strategies of the game and the theory of quantum permutation groups. We identify a key property of this game that is central to many results about it. We call games with this property bisynchronous. In this talk, we introduce these games and the corre-sponding correlations arising from the perfect winning strategies for such games. Moreover, when the number of inputs is equal to the number of outputs, each bisynchronous correlation gives rise to a unital quantum channel which will be shown to be factorizable in the sense of Haagerup-Musat. Motivated from this nding, we further generalize the concept of factorizability and introduce a new class of quantum channels that we call positively factorizable. It turns out that there is a close connection be-tween the convex sets in Euclidian space containing self-dual cones and the existence of these maps. In this context, we nd new examples of matrices which are non-negative but not CPSD (completely positive semidenite). This talk is based on two separate works with Vern Pauls.
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