Construction of Sets of Orthogonal Quantum States with Minimal Nonlocality in Bipartite and Tripartite Systems of Unequal Local Dimensions

Abstract:The research on minimal nonlocality aims to determine the minimal cardinality of nonlocal sets of quantum states. However, the construction of a nonlocal set of states in bipartite or tripartite quantum systems with unequal local dimensions remains unsolved. In this paper, we first give a method to construct a set of orthogonal quantum states with minimal nonlocality in $\mathbb{C}^{4} \otimes \mathbb{C}^{7}$ quantum system. Then we give a general method to construct a set of orthogonal quantum states with minimal nonlocality in a bipartite quantum system with unequal local dimensions. Furthermore, we generalize the construction method to tripartite quantum system with unequal local dimensions, and construct a set of orthogonal quantum states with minimal nonlocality in $\mathbb C^{d_1} \otimes \mathbb C^{d_2}\otimes \mathbb C^{d_3}$ quantum system for $5\le d_1 < d_2 < d_3$. Our work settles the construction problem of a set of orthogonal states with minimal nonlocality in both bipartite and tripartite systems with unequal local dimensions.

arXiv:2607.28998 [quant-ph]

(or arXiv:2607.28998v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.28998 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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