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We analyze optimal schemes and also propose some practical schemes for thenonlocal conversion from two shared Bell pairs to four-qubit entangled statesin optical quantum networks. In the analysis, we consider two-qubit operationsas nonlocal operations and minimize the number of access to ancillary qubits aspossible. First, we consider two-qubit unitary operations without usingancillary qubits and derive a necessary and sufficient condition forconvertible states. Second, we consider nonlocal optical systems composed ofpassive linear optics and postselection. For the passive linear opticalsystems, we derive achievable upper bounds of success probabilities of theconversion in the case without ancillary qubits. We also compare the optimalsuccess probabilities with those of previously proposed schemes. Finally, wediscuss success probabilities of the conversion in the case with ancillaryqubits.

Optimal nonlocal conversion of photonic four-partite entanglement from two Bell pairs in quantum networks