Generalized W state of four qubits with exclusively the three-tangle

Abstract

We single out a class of states possessing only threetangle but distributed all over four qubits. This is a three-site analogue of states from the W -class, which only possess globally distributed pairwise entanglement as measured by the concurrence. We perform an analysis for four qubits, showing that such a state indeed exists. To this end we analyze specific states of four qubits that are not convexly balanced as for SL invariant families of entanglement, but only affinely balanced. For these states all possible SL-invariants vanish, hence they are part of the SL null-cone. Instead, they will possess at least a certain unitary invariant.As an interesting byproduct it is demonstrated that the exact convex roof is reached in the ranktwo case of a homogeneous polynomial SL-invariant measure of entanglement of degree 2m, if there is a state which corresponds to a maximally m-fold degenerate solution in the zero-polytope that can be combined with the convexified minimal characteristic curve to give a decomposition of ρ. If more than one such state does exist in the zero polytope, a minimization must be performed. A better lower bound than the lowest convexified characteristic curve is obtained if no decomposition of ρ is obtained in this way.

Tetrapartite entanglement features of W-Class state in uniform acceleration

“…Its main aim is to incorporate relativistic effects to improve quantum-information tasks and to understand how such protocols will happen in curved space times. Since tripartite entangled state was worked out [19] and the Unruh effect was studied, most of the papers focus their investigation in two main states, i.e., Greenberger-Horne-Zeilinger (GHZ), W-state and other related states, but the W-state with less study due to the complexity of their calculations [34][35][36][37][38][39]. It should be pointed out that the computation of entanglement for the tripartite pure or mixed state in an accelerated frame is much more complicated because the density matrix cannot be written as the form of an X matrix.…”

Tetrapartite entanglement measures of GHZ state with uniform acceleration

“…the GHZ and W-state, and other related states. Among them, the W-state is less studied because of its complexity [38][39][40][41][42][43][44][45]. Most contributions to this topic are related to their density matrices with the form of an X matrix.…”