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

• URL: http://arxiv.org/abs/2607.28998v1
• Date: Fri, 31 Jul 2026 03:52:55 GMT
• Title: Construction of Sets of Orthogonal Quantum States with Minimal Nonlocality in Bipartite and Tripartite Systems of Unequal Local Dimensions
• Abstract summary: The research on minimal nonlocality aims to determine the minimal cardinality of nonlocal sets of quantum states.<n>The construction of a nonlocal set of states in bipartite or tripartite quantum systems with unequal local dimensions remains unsolved.
• Score: 2.4352431518568114
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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