Entanglement of Four-Qubit Rank-$2$ Mixed States

Abstract

It is known that there are three maximally entangled states $|{\Phi }_1⟩=(|0000⟩+|1111⟩)/\sqrt{2}$, $|{\Phi }_2⟩=(\sqrt{2}|1111⟩+|1000⟩+|0100⟩+|0010⟩+|0001⟩)/\sqrt{6}$, and $|{\Phi }_3⟩=(|1111⟩+|1100⟩+|0010⟩+|0001⟩)/2$ in four-qubit system. It is also known that there are three independent measures ${\mathcal{F}}_j^{(4)}(j=1,2,3)$ for true four-way quantum entanglement in the same system. In this paper we compute ${\mathcal{F}}_j^{(4)}$ and their corresponding linear monotones ${\mathcal{G}}_j^{(4)}$ for three rank-two mixed states $ρ_j = p \ket{Φ_j}\bra{Φ_j} + (1 - p) \ket{\mbox{W}_4} \bra{\mbox{W}_4}$, where $\ket{\mbox{W}_4} = (\ket{0111} + \ket{1011} + \ket{1101} + \ket{1110}) / 2$. We discuss the possible applications of our results briefly.

20 pages, 5 eps figures, will appear in Quantum Information Processing

References in corpus (2)

• Constructing N-qubit entanglement monotones from anti-linear operators
• Tangles of superpositions and the convex-roof extension