Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When Do Composed Maps Become Entanglement Breaking?   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
parts of quantum information theory, and we prove the conjecture for Gaussian
quantum channels.

18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org