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Communications in Theoretical Physics

Criterion of Quantum Entanglement and the Covariance Correlation Tensor in the Theory of Quantum Network

Qian Shang-Wu, Gu Zhi-Yu

Published Jan 15, 2003• 7 citations
Publisher

Abstract

This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of nodes.

DOI
10.1088/0253-6102/39/1/15

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This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of nodes.
By using the block division method in matrix calculus, this article successfully calculate the expectation values of the generating operators and the correlation tensors for quantum network of any nodes. Thence, by means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory, this article discusses the complete and partial separability conditions of the mixed quantum state for a quantum network of any nodes and judge the separability of a quantum state in the general case of any nodes for two examples.