It is known that there are three maximally entangled states $$|\varPhi _1 \rangle = (|0000 \rangle + |1111 \rangle ) / \sqrt{2}$$ | Φ 1 ⟩ = ( | 0000 ⟩ + | 1111 ⟩ ) / 2 , $$|\varPhi _2 \rangle = (\sqrt{2} |1111 \rangle + |1000 \rangle + |0100 \rangle + |0010 \rangle + |0001 \rangle ) / \sqrt{6}$$ | Φ 2 ⟩ = ( 2 | 1111 ⟩ + | 1000 ⟩ + | 0100 ⟩ + | 0010 ⟩ + | 0001 ⟩ ) / 6 , and $$|\varPhi _3 \rangle = (|1111 \rangle + |1100 \rangle + |0010 \rangle + |0001 \rangle ) / 2$$ | Φ 3 ⟩ = ( | 1111 ⟩ + | 1100 ⟩ + | 0010 ⟩ + | 0001 ⟩ ) / 2 in four-qubit system. It is also known that there are three independent measures $$\mathcal{F}^{(4)}_j (j=1,2,3)$$ F j ( 4 ) ( j = 1 , 2 , 3 ) for true four-way quantum entanglement in the same system. In this paper, we compute $$\mathcal{F}^{(4)}_j$$ F j ( 4 ) and their corresponding linear monotones $$\mathcal{G}^{(4)}_j$$ G j ( 4 ) for three rank-two mixed states $$\rho _j = p |\varPhi _j \rangle \langle \varPhi _j | + (1 - p) |\text{ W }_4 \rangle \langle \text{ W }_4 |$$ ρ j = p | Φ j ⟩ ⟨ Φ j | + ( 1 - p ) | W 4 ⟩ ⟨ W 4 | , where $$|\text{ W }_4 \rangle = (|0111 \rangle + |1011 \rangle + |1101 \rangle + |1110 \rangle ) / 2$$ | W 4 ⟩ = ( | 0111 ⟩ + | 1011 ⟩ + | 1101 ⟩ + | 1110 ⟩ ) / 2 . We discuss the possible applications of our results briefly.
Quantum Information Processing – Springer Journals
Published: Jun 11, 2015
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