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When Do Composed Maps Become Entanglement Breaking?. (arXiv:1807.01266v1 [quant-ph])
来源于:arXiv
For many completely positive maps repeated compositions will eventually
become entanglement breaking. To quantify this behaviour we develop a technique
based on the Schmidt number: If a completely positive map breaks the
entanglement with respect to any qubit ancilla, then applying it to part of a
bipartite quantum state will result in a Schmidt number bounded away from the
maximum possible value. Iterating this result puts a successively decreasing
upper bound on the Schmidt number arising in this way from compositions of such
a map. By applying this technique to completely positive maps in dimension
three that are also completely copositive we prove the so called PPT squared
conjecture in this dimension. We then give more examples of completely positive
maps where our technique can be applied, e.g.~maps close to the completely
depolarizing map, and maps of low rank. Finally, we study the PPT squared
conjecture in more detail, establishing equivalent conjectures related to other
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