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A quantum theory of nearly degenerate backward four-wave mixing in a two-level atomic system is developed. The theory is used to calculate the quantum noise produced by a phase-conjugate mirror based on this system. The results indicate that in the case of pure radiative broadening the ideal quantum-noise limit is reached for relatively small pump-wave strengths and for relatively large probe-pump and pump-resonance detunings, so that the phase-conjugate reflectivity is far from its maximumdoi:10.1103/physreva.55.3155 fatcat:kq7h5hvq6fge7euqb5yz3jdonm