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Positivity of linear maps under tensor powers

Alexander Müller-Hermes, David Reeb, Michael M. Wolf

J. Math. Phys. 57, 015202 , (2016)

arXiv.org: 1502.05630 Pfeil

Abstract: We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n∈N there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions we reduce the existence question of such non-trivial