The interaction of a five-level atomic system involving electromagnetically induced transparency with four light fields is investigated. Two different operating regimes are considered, semi-classical and quantized, where two light fields are treated as quantum. In the semi-classical regime, the dispersive properties of the scheme are analyzed in detail, and the conditions leading to group velocity matching for two of the light fields are identified. In the quantized regime, the two quantum fields undergo cross-phase modulation induced by electromagnetically induced transparency. Based on this, a recent proposal [C. Ottaviani et al., Phys. Rev. A 73, 010301 (R) (2006)] for a two-qubit quantum phase gate for traveling single-photon qubits is examined. An experimental scheme for verification of QPG operation is proposed.