  We design optimal interferometric schemes for implementation of two-qubit
linear optical quantum filters diagonal in the computational basis. The
filtering is realized by interference of the two photons encoding the qubits in
a multiport linear optical interferometer, followed by conditioning on presence
of a single photon in each output port of the filter. The filter thus operates
in the coincidence basis, similarly to many linear optical unitary quantum
gates. Implementation of the filter with linear optics may require an
additional overhead in terms of reduced overall success probability of the
filtering and the optimal filters are those that maximize the overall success
probability. We discuss in detail the case of symmetric real filters and extend
our analysis also to asymmetric and complex filters.
