Fidelity of photon propagation in electromagnetically induced transparency in the presence of four-wave mixing

We study the effects of four-wave mixing (4WM) in a quantum memory scheme based on electromagnetically induced transparency (EIT). We treat the problem of field propagation on the quantum mechanical level, which allows us to calculate the fidelity of propagation for a quantum light pulse such as a single photon. While 4WM can be beneficial for classical, all-optical information storage, the quantum noise associated with the signal amplification and idler generation is, in general, detrimental for a quantum memory. We identify a range of parameters where 4WM makes a single-photon quantum memory impossible.