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arXiv:1208.3588 · Reports on Mathematical Physics

Monogamous Property of Generalized W States in Three-Qubit Systems in Terms of Relative Entropy of Entanglement

Zhen Wang, Xiu-Hong Gao, Zhi-Xi Wang

Published Oct 1, 2012• 2 citations
arXivHTMLPDF
DOI
10.1016/s0034-4877(12)60042-1

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The monogamy of entanglement is generally discussed using a bipartite entanglement measure as an upper bound. Here we discuss a new kind of monogamous relation where the upper bound is given by a multipartite measure of entanglement, the generalized concurrence. We show a monogamous equality involving the multipartite concurrence, all the bipartite concurrences, and the genuine tripartite entanglement for pure three-qubit systems. The result extends to mixed states in an inequality involving the generalized concurrence and all the bipartite concurrences. We provide a counterexample showing that the result cannot be extended for systems with more than three qubits.
We present the modified relative entropy of entanglement for multi-party systems by a given relative density matrix which is spanned by a linear combination of the direct products of so-called basis of relative density matrices and reduced density matrices for every party. For three qubit system in a pure state we derive out the explicit and closed expression of our relative density matrix which is a function of the components of the state vector of three qubits. Through computing the modified relative entropy of entanglement of some important and interesting examples, we display the main behaviors and elementary properties of the modified relative entropy of entanglement and compare it with the generalized entanglement of formation. Moreover, we also propose an assistant, as the upper bound, of the modified relative entropy of entanglement.