Partial K-way negativities and three tangle for three qubit states

Abstract

We obtain, analytically, the global negativity, partial $K-$way negativities (K=2, 3), Wooter's tangle and three tangle for the generic three qubit canonical state. It is found that the product of global negativity and partial three way negativity is equal to three tangle, while the partial two way negativity is related to tangle of qubit pairs. We also calculate similar quantities for the state canonical to a single parameter (0<q<1) pure state which is a linear combination of a GHZ state and a W state. In this case for q=0.62685, the state has zero three tangle and zero three-way negativity, having only W-like entanglement. The difference between the product of global and partial three way negativity and three tangle for a given state is a quantitative measure of two qubit coherences transformed by unitary transformations on canonical state into three qubit coherences. The global negativity and partial K-way negativities, obtained by selective partial transpositions on multi-qubit state operator, satisfy inequalities which for three qubits are equivalent to CKW (Coffman-Kundu-Wootter) inequality.

07 pages, revtex, typos corrected

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• Unitary Invariants and Classification of Four-Qubit States via Negativity Fonts
• Generation of field mediated three qubit entangled state shared by Alice and Bob
• Partial K-way Negativities of Pure Four qubit Entangled States
• Negativity Fonts, multiqubit invariants and Four qubit Maximally Entangled States
• Sequential generation of Polynomial Invariants and N-body non-local correlations