Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911882589241344 |
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| author | He, Yiyun Shi, Fei Zhang, Xiande |
| author_facet | He, Yiyun Shi, Fei Zhang, Xiande |
| contents | A set of orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. Although such a phenomenon has been shown to any three-, four-, and five-partite systems, the existence of strongly nonlocal orthogonal product sets in multipartite systems remains unknown. In this paper, by using a general decomposition of the $N$-dimensional hypercubes, we present strongly nonlocal orthogonal product sets in $N$-partite systems for all odd $N\geq 3$. Based on this decomposition, we give explicit constructions of unextendible product bases in $N$-partite systems for odd $N\geq 3$. Furthermore, we apply our results to quantum secret sharing, uncompletable product bases, and PPT entangled states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_14503 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$ He, Yiyun Shi, Fei Zhang, Xiande Quantum Physics A set of orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. Although such a phenomenon has been shown to any three-, four-, and five-partite systems, the existence of strongly nonlocal orthogonal product sets in multipartite systems remains unknown. In this paper, by using a general decomposition of the $N$-dimensional hypercubes, we present strongly nonlocal orthogonal product sets in $N$-partite systems for all odd $N\geq 3$. Based on this decomposition, we give explicit constructions of unextendible product bases in $N$-partite systems for odd $N\geq 3$. Furthermore, we apply our results to quantum secret sharing, uncompletable product bases, and PPT entangled states. |
| title | Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$ |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2203.14503 |