Probabilistic catalyzed entanglement concentration of qubit pairs

We analytically obtain the maximum probability of converting a finite number of copies of an arbitrary two-qubit pure state to a single copy of a maximally entangled two-qubit pure state via entanglement-assisted local operations and classical communications using a two-qubit catalyst state, which may be destroyed when the conversion fails. We show that the optimal catalyst for this transformation is always more entangled than the initial state but any two-qubit state can act as a (non-optimal) catalyst. Interestingly, the entanglement of the optimal two-qubit catalyst state is shown to decrease with that of the initial state. The unitaries and measurements required for catalytic entanglement concentration are presented.