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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 rank-two 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 $rho$. 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 $rho$ is obtained in this way.
I calculate the mixed threetangle $tau_3[rho]$ for the reduced density matrices of the four-qubit representant states found in Phys. Rev. A {bf 65}, 052112 (2002). In most of the cases, the convex roof is obtained, except for one class, where I provi
We introduce a new measure for the genuinely N-partite (all-party) entanglement of N-qubit states using the trace distance metric, and find an algebraic formula for the GHZ-diagonal states. We then use this formula to show how the all-party entanglem
We investigate possible generalizations of the Coffman-Kundu-Wootters monogamy inequality to four qubits, accounting for multipartite entanglement in addition to the bipartite terms. We show that the most natural extension of the inequality does not
We study the dynamics of four-qubit W state under various noisy environments by solving analytically the master equation in the Lindblad form in which the Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Als
Progress in superconducting qubit experiments with greater numbers of qubits or advanced techniques such as feedback requires faster and more accurate state measurement. We have designed a multiplexed measurement system with a bandpass filter that al