Entanglement optimizing mixtures of two-qubit states

Entanglement in incoherent mixtures of pure states of two qubits is considered via the concurrence measure. A set of pure states is optimal if the concurrence for any mixture of them is the weighted sum of the concurrences of the generating states. When two or three pure real states are mixed, it is shown that 28.5% or 5.12% of the cases, respectively, are optimal. Conditions that are obeyed by the pure states generating such optimally entangled mixtures are derived. For four or more pure states, it is shown that there are no such sets of real states. The implication of these on the superposition of two or more dimerized states is discussed. A corollary of these results also show in how many cases rebit concurrence can be the same as that of qubit concurrence. © 2011 IOP Publishing Ltd.