Impossibility of local state transformation via hypercontractivity
Can a target bipartite quantum state \(\sigma_{A'B'}\) be obtained by applying local operations to (arbitrarily many) \(n\) copies of a given bipartite state \(\rho_{AB}\)? Necessary conditions for a positive answer are given in terms of hypercontractivity properties of superoperators related to duly ``normalized'' states \(\tilde{\rho}^{\otimes n}\) and \(\tilde{\sigma}\) via Choi-Jamiolkowski correspondence. The superoperators are endowed with norms and completely bounded norms, with respect to the scales of Schatten spaces, to analyze the arising hypercontractivity ribbons. The latter notion was known in the classical case, as well as maximal correlation, and both are generalized to the noncommutative quantum setting to provide measures of bipartite correlation. Illustrative examples are also given.
scientific article; zbMATH DE number 6353812
scientific article