  We study the effects of the 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 for 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.
