Bounds On The Smallest Sets Of Quantum States With Special Quantum Nonlocality

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Bounds on the smallest sets of quantum states with special quantum nonlocality PlatoBlockchain Data Intelligence. Vertical Search. Ai.

Mao-Sheng Li¹ and Yan-Ling Wang²

¹School of Mathematics, South China University of Technology, Guangzhou 510641, China
²School of Computer Science and Technology, Dongguan University of Technology, Dongguan, 523808, China

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Abstract

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 [46]. 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 $1leq ileq N$?) raised in a recent paper [54]. Compared with all previous relevant proofs, our proof here is quite concise.

► BibTeX data

@article{Li2023boundssmallestsets, doi = {10.22331/q-2023-09-07-1101}, url = {https://doi.org/10.22331/q-2023-09-07-1101}, title = {Bounds on the smallest sets of quantum states with special quantum nonlocality}, author = {Li, Mao-Sheng and Wang, Yan-Ling}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1101}, month = sep, year = {2023}<br /> }

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Cited by

[1] Zong-Xing Xiong and Yongli Zhang, “Genuine nonlocality of generalized GHZ states in many-partite systems”, arXiv:2308.07171, (2023).

[2] Zong-Xing Xiong, Mao-Sheng Li, Zhu-Jun Zheng, and Lvzhou Li, “Distinguishability-based genuine nonlocality with genuine multipartite entanglement”, Physical Review A 108 2, 022405 (2023).

[3] Mengying Hu, Ting Gao, and Fengli Yan, “Strong quantum nonlocality with genuine entanglement in an $N$-qutrit system”, arXiv:2308.16409, (2023).

[4] Hai-Qing Cao and Hui-Juan Zuo, “Locally distinguishing nonlocal sets with entanglement resource”, Physica A Statistical Mechanics and its Applications 623, 128852 (2023).

[5] Huaqi Zhou, Ting Gao, and Fengli Yan, “Orthogonal product sets with strong quantum nonlocality on a plane structure”, Physical Review A 106 5, 052209 (2022).

[6] Yan-Ling Wang, Wei Chen, and Mao-Sheng Li, “Small set of orthogonal product states with nonlocality”, Quantum Information Processing 22 1, 15 (2023).

[7] Yan-Ying Zhu, Dong-Huan Jiang, Guang-Bao Xu, and Yu-Guang Yang, “Completable sets of orthogonal product states with minimal nonlocality”, Physica A Statistical Mechanics and its Applications 624, 128956 (2023).

[8] Ying-Hui Yang, Guang-Wei Mi, Shi-Jiao Geng, Qian-Qian Liu, and Hui-Juan Zuo, “Strong nonlocality with genuine entanglement based on GHZ-like states in multipartite quantum systems”, Physica Scripta 98 1, 015104 (2023).

[9] Hai-Qing Cao, Mao-Sheng Li, and Hui-Juan Zuo, “Locally stable sets with minimum cardinality”, Physical Review A 108 1, 012418 (2023).

[10] Wang Yan-Ling, Chen Wei, and Li Mao-Sheng, “Small set of orthogonal product states with nonlocality”, arXiv:2207.04603, (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2023-09-08 02:19:12). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-09-08 02:19:11).

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Source: https://quantum-journal.org/papers/q-2023-09-07-1101/

Time Stamp: September 7, 2023

Time Stamp: Dec 14, 2023

Republished By Plato

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