Separability Criteria of Quantum States based on Generalized Bloch Representation

• URL: http://arxiv.org/abs/2510.24110v1
• Date: Tue, 28 Oct 2025 06:29:06 GMT
• Title: Separability Criteria of Quantum States based on Generalized Bloch Representation
• Authors: Linwei Li, Hongmei Yao, Chunlin Yang, Shaoming Fei,
• Abstract summary: Quantum entanglement serves as a fundamental resource in quantum information theory.<n>This paper presents a comprehensive framework of separability criteria for detecting entanglement across quantum systems.<n> Numerical examples demonstrate that our separability criteria exhibit enhanced capability in detecting entanglement.
• Score: 1.886547784768222
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum entanglement serves as a fundamental resource in quantum information theory. This paper presents a comprehensive framework of separability criteria for detecting entanglement across quantum systems, from bipartite to multipartite states. We propose a novel unified parameterized extended correlation tensor, constructed via the generalized Bloch representation under an arbitrary orthogonal basis, which bridges our bipartite criterion with several existing ones. Moreover, we develop a specialized tensor unfolding technique -- termed mixed mode matrix unfolding -- that naturally generalizes the conventional $k$-mode matrix unfolding and enables the generalization of the extended correlation tensor construction to multipartite systems. And we derive several separability criteria for multipartite states. Numerical examples demonstrate that our separability criteria exhibit enhanced capability in detecting entanglement.

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