  We analyze the nonlinear optical response of a six-level atomic system under
a configuration of electromagnetically induced transparency. The giant
fifth-order nonlinearity generated in such a system with a relatively large
cross-phase modulation effect can produce efficient three-way entanglement and
may be used for realizing a three-qubit quantum phase gate. We demonstrate that
such phase gate can be transferred to a Toffoli gate, facilitating practical
applications in quantum information and computation.
