Three-qubit quantum gates and filters for linear optical quantum-information processing

We present a linear optical scheme for the implementation of a three-qubit quantum gate that can be considered as a generalization of the two-qubit partial-SWAP gate. The gate leaves unchanged all fully symmetric states of three qubits, and all states antisymmetric with respect to the transposition of some pair of qubits acquire a phase shift phi. The gate operates in the coincidence basis and requires one auxiliary pair of photons prepared in the maximally entangled Bell state. By altering parameters of the proposed interferometric scheme, we can also obtain a quantum filter that attenuates amplitudes of the three-qubit states according to their permutation symmetry properties.