Three-Way Entanglement and Three-Qubit Phase Gate Based on a Coherent Six-Level Atomic System

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.