Bounds on the smallest sets of quantum states with special quantum nonlocality
An orthogonal set of states in multipartite systems is called to be strong quantum nonlocality if it is locally irreducible under every bipartition of the subsystems \cite{Halder19}. In this work, we study a subclass of locally irreducible sets: the only possible orthogonality preserving measuremen...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-09-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-09-07-1101/pdf/ |
| _version_ | 1797690570128228352 |
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| author | Mao-Sheng Li Yan-Ling Wang |
| author_facet | Mao-Sheng Li Yan-Ling Wang |
| author_sort | Mao-Sheng Li |
| collection | DOAJ |
| description | An orthogonal set of states in multipartite systems is called to be strong quantum nonlocality if it is locally irreducible under every bipartition of the subsystems \cite{Halder19}. In this work, we study a subclass of locally irreducible sets: the only possible orthogonality preserving measurement on each subsystems are trivial measurements. We call the set with this property is locally stable. We find that in the case of two qubits systems locally stable sets are coincide with locally indistinguishable sets. Then we present a characterization of locally stable sets via the dimensions of some states depended spaces. Moreover, we construct two orthogonal sets in general multipartite quantum systems which are locally stable under every bipartition of the subsystems. As a consequence, we obtain a lower bound and an upper bound on the size of the smallest set which is locally stable for each bipartition of the subsystems. Our results provide a complete answer to an open question (that is, can we show strong quantum nonlocality in $\mathbb{C}^{d_1} \otimes \mathbb{C}^{d_1}\otimes \cdots \otimes \mathbb{C}^{d_N} $ for any $d_i \geq 2$ and $1\leq i\leq N$?) raised in a recent paper \cite{Shi22N}. Compared with all previous relevant proofs, our proof here is quite concise. |
| first_indexed | 2024-03-12T02:01:13Z |
| format | Article |
| id | doaj.art-61e91c9b60da439aa38c263cf0178cc5 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-12T02:01:13Z |
| publishDate | 2023-09-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-61e91c9b60da439aa38c263cf0178cc52023-09-07T14:19:38ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-09-017110110.22331/q-2023-09-07-110110.22331/q-2023-09-07-1101Bounds on the smallest sets of quantum states with special quantum nonlocalityMao-Sheng LiYan-Ling WangAn orthogonal set of states in multipartite systems is called to be strong quantum nonlocality if it is locally irreducible under every bipartition of the subsystems \cite{Halder19}. In this work, we study a subclass of locally irreducible sets: the only possible orthogonality preserving measurement on each subsystems are trivial measurements. We call the set with this property is locally stable. We find that in the case of two qubits systems locally stable sets are coincide with locally indistinguishable sets. Then we present a characterization of locally stable sets via the dimensions of some states depended spaces. Moreover, we construct two orthogonal sets in general multipartite quantum systems which are locally stable under every bipartition of the subsystems. As a consequence, we obtain a lower bound and an upper bound on the size of the smallest set which is locally stable for each bipartition of the subsystems. Our results provide a complete answer to an open question (that is, can we show strong quantum nonlocality in $\mathbb{C}^{d_1} \otimes \mathbb{C}^{d_1}\otimes \cdots \otimes \mathbb{C}^{d_N} $ for any $d_i \geq 2$ and $1\leq i\leq N$?) raised in a recent paper \cite{Shi22N}. Compared with all previous relevant proofs, our proof here is quite concise.https://quantum-journal.org/papers/q-2023-09-07-1101/pdf/ |
| spellingShingle | Mao-Sheng Li Yan-Ling Wang Bounds on the smallest sets of quantum states with special quantum nonlocality Quantum |
| title | Bounds on the smallest sets of quantum states with special quantum nonlocality |
| title_full | Bounds on the smallest sets of quantum states with special quantum nonlocality |
| title_fullStr | Bounds on the smallest sets of quantum states with special quantum nonlocality |
| title_full_unstemmed | Bounds on the smallest sets of quantum states with special quantum nonlocality |
| title_short | Bounds on the smallest sets of quantum states with special quantum nonlocality |
| title_sort | bounds on the smallest sets of quantum states with special quantum nonlocality |
| url | https://quantum-journal.org/papers/q-2023-09-07-1101/pdf/ |
| work_keys_str_mv | AT maoshengli boundsonthesmallestsetsofquantumstateswithspecialquantumnonlocality AT yanlingwang boundsonthesmallestsetsofquantumstateswithspecialquantumnonlocality |