Distribution of spin correlation strengths in multipartite systems
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For a two-qubit state, the isotropic strength measures the degree of isotropic spin correlation. The concept of isotropic strength is generalized to multipartite qudit systems, and the strength distributions for tripartite and quadripartite qudit systems are thoroughly investigated. We show that the sum of relative isotropic strengths of any three-qudit state over d-dimensional Hilbert space cannot exceed \(d-1\), which generalizes the case \(d=2\). The trade-off relations and monogamy-like relations of the sum of spin correlation strengths for pure three- and four-partite systems are derived. Moreover, the bounds of spin correlation strengths among different subsystems of a quadripartite state are used to analyze quantum entanglement.
We thank Jun Li for helpful discussions on entanglement detection and related problems. This work is partially supported by National Natural Science Foundation Grant No. 11531004, Simons Foundation Grant No. 523868 and a grant from China Scholarship Council.