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