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We propose and investigate a method to optimize recurrence entanglementpurification protocols. The approach is based on a numerical search in thewhole set of SU(4) matrices with the aid of a quasi-Newton algorithm. Ourmethod evaluates average concurrences where the probabilistic occurrence ofmixed entangled states is also taken into account. We show for certain familiesof states that optimal protocols are not necessarily achieved by bilaterallyapplied controlled-NOT gates. As we discover several optimal solutions, theproposed method offers some flexibility in experimental implementations ofentanglement purification protocols and interesting perspectives in quantuminformation processing.

Optimal two-qubit gates in recurrence protocols of entanglement purification