In this report, we calculate the three tangle of assistance and give the corresponding best possible pure state decomposition of rank-two mixed states for the three-qubit Greenberger-Horne-Zeilinger (GHZ) state and $W$ state. As the three tangle can be transformed into bipartite concurrence with assistance, we achieve a lower bound of the assisted concurrence with local operations and classical communication (LOCC) constraints via these pure state decompositions. It is smaller than the total assisted concurrence, which shows that local assistance alone is not sufficient for maximizing bipartite entanglement. The increase of three tangle is attributed to the genuine multipartite entanglement in the purified state. A genuine four-qubit entanglement measure is calculated for the purified four-qubit state and compared to the three tangle of assistance.In this report, we calculate the three tangle of assistance and give the corresponding best possible pure state decomposition of rank-two mixed states for the three-qubit Greenberger-Horne-Zeilinger (GHZ) state and $W$ state. As the three tangle can be transformed into bipartite concurrence with assistance, we achieve a lower bound of the assisted concurrence with local operations and classical communication (LOCC) constraints via these pure state decompositions. It is smaller than the total assisted concurrence, which shows that local assistance alone is not sufficient for maximizing bipartite entanglement. The increase of three tangle is attributed to the genuine multipartite entanglement in the purified state. A genuine four-qubit entanglement measure is calculated for the purified four-qubit state and compared to the three tangle of assistance.

Physical Review AApr 13, 20103 citations

Three-tangle for rank-three mixed states: Mixture of Greenberger-Horne-Zeilinger, W , and flipped- W states

Eylee Jung, Mi-Ra Hwang, DaeKil Park +1 more

Three-tangle for a rank-3 mixture composed of Greenberger-Horne-Zeilinger, $W$ , and flipped- $W$ states is analytically calculated. The optimal decompositions in the full range of parameter space are constructed by making use of the convex-roof extension. We also provide an analytical technique, which determines whether or not an arbitrary rank-3 state has vanishing three-tangle. This technique is developed by making use of the Bloch sphere ${S}^{8}$ of the qutrit system. The Coffman-Kundu-Wootters inequality is discussed by computing one-tangle and concurrences. It is shown that the one-tangle is always larger than the sum of squared concurrences and three-tangle. The physical implication of three-tangle is briefly discussed.Three-tangle for a rank-3 mixture composed of Greenberger-Horne-Zeilinger, $W$, and flipped-$W$ states is analytically calculated. The optimal decompositions in the full range of parameter space are constructed by making use of the convex-roof extension. We also provide an analytical technique, which determines whether or not an arbitrary rank-3 state has vanishing three-tangle. This technique is developed by making use of the Bloch sphere ${S}^{8}$ of the qutrit system. The Coffman-Kundu-Wootters inequality is discussed by computing one-tangle and concurrences. It is shown that the one-tangle is always larger than the sum of squared concurrences and three-tangle. The physical implication of three-tangle is briefly discussed.

arXiv:0810.5403Physical Review AFeb 11, 200948 citations

Five-Dimensional Compatibility and Stratified Local-Unitary Structure of Pure Three-Qubit States

Wei Song, Xiao-Lan Zong, Ming Yang

We investigates the joint compatibility problem of the three pairwise concurrences, the three-tangle, and the Kempe invariant in arbitrary pure three-qubit states, and gives necessary and sufficient conditions for these five quantities to be simultaneously realizable by the same pure state. This five-dimensional compatibility region can be viewed as a fiber structure over the previously derived four-dimensional reachable region. We further find that the residual continuous local-unitary freedom depends on the position of the state within this region. In the generic interior, one continuous degree of freedom remains. It is fixed if the three-tangle vanishes or a pairwise concurrence becomes zero, and also at the boundary of the four-dimensional tangle region. The Kempe invariant gives the simplest algebraic parametrization of the fifth coordinate, but the same degree of freedom may be described by a known pure-state entanglement monotone. The compatibility conditions can also be expressed in terms of concurrence-based bipartite measures and multipartite quantities fixed by the pairwise concurrences and the three-tangle.We investigates the joint compatibility problem of the three pairwise concurrences, the three-tangle, and the Kempe invariant in arbitrary pure three-qubit states, and gives necessary and sufficient conditions for these five quantities to be simultaneously realizable by the same pure state. This five-dimensional compatibility region can be viewed as a fiber structure over the previously derived four-dimensional reachable region. We further find that the residual continuous local-unitary freedom depends on the position of the state within this region. In the generic interior, one continuous degree of freedom remains. It is fixed if the three-tangle vanishes or a pairwise concurrence becomes zero, and also at the boundary of the four-dimensional tangle region. The Kempe invariant gives the simplest algebraic parametrization of the fifth coordinate, but the same degree of freedom may be described by a known pure-state entanglement monotone. The compatibility conditions can also be expressed in terms of concurrence-based bipartite measures and multipartite quantities fixed by the pairwise concurrences and the three-tangle.

quant-pharXiv:2609.03864Sep 4, 20260 citations

Entanglement à trois

Geoff J. Pryde

Nature PhotonicsMar 28, 20140 citations

Typical entanglement

Fabio Deelan Cunden, Paolo Facchi A, Giuseppe Florio +1 more

arXiv:1303.4209The European Physical Journal PlusMay 1, 20139 citations

W

state. As the three tangle can be transformed into bipartite concurrence with assistance, we achieve a lower bound of the assisted concurrence with local operations and classical communication (LOCC) constraints via these pure state decompositions. It is smaller than the total assisted concurrence, which shows that local assistance alone is not sufficient for maximizing bipartite entanglement. The increase of three tangle is attributed to the genuine multipartite entanglement in the purified state. A genuine four-qubit entanglement measure is calculated for the purified four-qubit state and compared to the three tangle of assistance.

Three-tangle for a rank-3 mixture composed of Greenberger-Horne-Zeilinger,

W

, and flipped-

W

states is analytically calculated. The optimal decompositions in the full range of parameter space are constructed by making use of the convex-roof extension. We also provide an analytical technique, which determines whether or not an arbitrary rank-3 state has vanishing three-tangle. This technique is developed by making use of the Bloch sphere

{S}^{8}

of the qutrit system. The Coffman-Kundu-Wootters inequality is discussed by computing one-tangle and concurrences. It is shown that the one-tangle is always larger than the sum of squared concurrences and three-tangle. The physical implication of three-tangle is briefly discussed.