1206.4113 (Sungguen Ryu et al.)

Minimax optimization of entanglement witness operator for the
quantification of three-qubit mixed-state entanglement    [PDF]

Sungguen Ryu, Seung-Sup B. Lee, H. -S. Sim

We develop a numerical approach for quantifying entanglement in mixed quantum states by convex-roof entanglement measures, based on the optimal entanglement witness operator and the minimax optimization method. Our new approach is applicable to general entanglement measures and states, and it is an efficient alternative to the conventional approach based upon the optimal pure-state decomposition. Compared with the conventional one, it has two important merits (i) that the global optimality of the solution is quantitatively verifiable, and (ii) that the optimization is considerably simplified by exploiting the common symmetry of the target state and measure. To demonstrate the merits, we quantify Greenberger-Horne-Zeilinger (GHZ) entanglement in a class of three-qubit full-rank mixed states composed of the GHZ state, the W state, and the white noise, the simplest mixtures of states with different genuine multipartite entanglement, which have not been quantified before this work. We discuss some general properties of the form of the optimal witness operator, and of the convex structure of mixed states, which are related to the symmetry and the rank of states.

View original: http://arxiv.org/abs/1206.4113