Decomposability of linear maps under tensor powers
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Decomposability of linear maps under tensor powers. / Mueller-Hermes, Alexander.
I: Journal of Mathematical Physics, Bind 59, Nr. 10, 102203 , 2018.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Decomposability of linear maps under tensor powers
AU - Mueller-Hermes, Alexander
PY - 2018
Y1 - 2018
N2 - Both completely positive and completely copositive maps stay decomposable under tensor powers, i.e., under tensoring the linear map with itself. But are there other examples of maps with this property? We show that this is not the case: Any decomposable map, that is neither completely positive nor completely copositive, will lose decomposability eventually after taking enough tensor powers. Moreover, we establish explicit bounds to quantify when this happens. To prove these results, we use a symmetrization technique from the theory of entanglement distillation and analyze when certain symmetric maps become non-decomposable after taking tensor powers. Finally, we apply our results to construct new examples of non-decomposable positive maps and establish a connection to the positive partial transpose squared conjecture.
AB - Both completely positive and completely copositive maps stay decomposable under tensor powers, i.e., under tensoring the linear map with itself. But are there other examples of maps with this property? We show that this is not the case: Any decomposable map, that is neither completely positive nor completely copositive, will lose decomposability eventually after taking enough tensor powers. Moreover, we establish explicit bounds to quantify when this happens. To prove these results, we use a symmetrization technique from the theory of entanglement distillation and analyze when certain symmetric maps become non-decomposable after taking tensor powers. Finally, we apply our results to construct new examples of non-decomposable positive maps and establish a connection to the positive partial transpose squared conjecture.
U2 - 10.1063/1.5045559
DO - 10.1063/1.5045559
M3 - Journal article
VL - 59
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 10
M1 - 102203
ER -
ID: 209166939