Global locations of Schmidt number witnesses
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914034957156352 |
|---|---|
| author | Han, Kyung Hoon Kye, Seung-Hyeok |
| author_facet | Han, Kyung Hoon Kye, Seung-Hyeok |
| contents | We investigate global locations of Schmidt number witnesses which are outside of the convex set of all bipartite states. Their locations are classified by interiors of faces of the convex set of all states, by considering the line segments from them to the maximally mixed state. In this way, a nonpositive Hermitian matrix of trace 1 is located outside of one and only one face. Faces of the convex set of all states are classified by subspaces, which are range spaces of states belonging to specific faces. For a given subspace, we show that there exist Schmidt number $k+1$ witnesses outside of the face arising from this subspace if and only if every vector in the orthogonal complement of the subspace has Schmidt rank greater than $k$. Once we have Schmidt number $k+1$ witnesses outside of a face, we also have Schmidt number $2,3,\dots, k$ witnesses outside of the face. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global locations of Schmidt number witnesses Han, Kyung Hoon Kye, Seung-Hyeok Quantum Physics We investigate global locations of Schmidt number witnesses which are outside of the convex set of all bipartite states. Their locations are classified by interiors of faces of the convex set of all states, by considering the line segments from them to the maximally mixed state. In this way, a nonpositive Hermitian matrix of trace 1 is located outside of one and only one face. Faces of the convex set of all states are classified by subspaces, which are range spaces of states belonging to specific faces. For a given subspace, we show that there exist Schmidt number $k+1$ witnesses outside of the face arising from this subspace if and only if every vector in the orthogonal complement of the subspace has Schmidt rank greater than $k$. Once we have Schmidt number $k+1$ witnesses outside of a face, we also have Schmidt number $2,3,\dots, k$ witnesses outside of the face. |
| title | Global locations of Schmidt number witnesses |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.10288 |