Halos and undecidability of tensor stable positive maps
A map P is tensor stable positive (tsp) if P⊗n is positive for all n, and essential tsp if it is not completely positive or completely co-positive. Are there essential tsp maps? Here we prove that there exist essential tsp maps on the hypercomplex numbers. It follows that there exist bound entangled...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10230/71750 |
| Acceso en línea: | http://hdl.handle.net/10230/71750 http://dx.doi.org/10.1088/1751-8121/ac726e |
| Access Level: | acceso abierto |
| Palabra clave: | Positive maps Tensor stable positivity Bound entanglement Undecidability Nonstandard numbers |
| Sumario: | A map P is tensor stable positive (tsp) if P⊗n is positive for all n, and essential tsp if it is not completely positive or completely co-positive. Are there essential tsp maps? Here we prove that there exist essential tsp maps on the hypercomplex numbers. It follows that there exist bound entangled states with a negative partial transpose (NPT) on the hypercomplex, that is, there exists NPT bound entanglement in the halo of quantum states. We also prove that tensor stable positivity on the matrix multiplication tensor is undecidable, and conjecture that tensor stable positivity is undecidable. Proving this conjecture would imply existence of essential tsp maps, and hence of NPT bound entangled states. |
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