BIRS Workshop Lecture Videos
Measuring quantum correlation via completely bounded norms Beigi, Salman
A hypercontractivity ribbon is a measure of bipartite correlation that is dened based on the operator norm of some linear map between Schatten classes that is associated to a given bipartite distribution. This measure of correlation has the intriguing property that the hypercontractivity ribbon of a bipartite distribution is equal to that of its i.i.d. repetitions. This talk is about the generalization of hypercontractivity ribbon for bipartite quantum states. We will discuss that to generalize the above property of the hypercontractivity ribbon to the quantum case we should use completely bounded norms. Then non-commutative vector valued Schatten spaces naturally appear in the study of quantum correlations. Finally we comment that these spaces also appear in the definition of a new generalization of Renyi (conditional) entropy to the quantum case.
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