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.
De Li Gao
De Rolf Gohm
De Aurelian Gheondea
De Ignacio Villanueva
De Michael Brannan
De Douglas Farenick
De David Pérez-García
De Yoshiko Ogata
De Runyao Duan
De Edward Effros
De Hiroyuki Osaka
De Fumio Hiai
De Magdalena Musat
De Nicholas LaRacuente
De Dan Voiculescu
De Aram Harrow
De Seung-Hyeok Kye
De Albert Schwarz
De Amine Marrakchi
De Juan Camilo Arosemena Serrato
De Albert Schwarz
De Juan Camilo Arosemena Serrato
De Francesca Arici
De Amine Marrakchi
