Completely entangled subspaces of entanglement depth $k$
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866913412675534848 |
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| author | Demianowicz, Maciej Vogtt, Kajetan Augusiak, Remigiusz |
| author_facet | Demianowicz, Maciej Vogtt, Kajetan Augusiak, Remigiusz |
| contents | We introduce a class of entangled subspaces: completely entangled subspaces of entanglement depth $k$ ($k$-CESs). These are subspaces of multipartite Hilbert spaces containing only pure states with an entanglement depth of at least $k$. We present an efficient construction of $k$-CESs of any achievable dimensionality in any multipartite scenario. Further, we discuss the relation between these subspaces and unextendible product bases (UPBs). In particular, we establish that there is a non-trivial bound on the cardinality of a UPB whose orthocomplement is a $k$-CES. Further, we discuss the existence of such UPBs for qubit systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08474 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Completely entangled subspaces of entanglement depth $k$ Demianowicz, Maciej Vogtt, Kajetan Augusiak, Remigiusz Quantum Physics We introduce a class of entangled subspaces: completely entangled subspaces of entanglement depth $k$ ($k$-CESs). These are subspaces of multipartite Hilbert spaces containing only pure states with an entanglement depth of at least $k$. We present an efficient construction of $k$-CESs of any achievable dimensionality in any multipartite scenario. Further, we discuss the relation between these subspaces and unextendible product bases (UPBs). In particular, we establish that there is a non-trivial bound on the cardinality of a UPB whose orthocomplement is a $k$-CES. Further, we discuss the existence of such UPBs for qubit systems. |
| title | Completely entangled subspaces of entanglement depth $k$ |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.08474 |