Appears in collection : Operator Algebras and Quantum Information Theory

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 natural number 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 “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of NPPT bound entanglement.