Controlled phase transformation of quantum states of an electromagnetic field in a high-quality cavity

This paper deals with the optical realization of a probabilistic operation of controlled phase transformation of three quantum modes of an electromagnetic field in a high-quality cavity. The required interaction between the modes is reached by a Rydberg atom passing through the cavity. The conditional Kraus operators formalism is used to estimate the atom-field interaction time and the coupling constants. Approximate values of the phase transformation probability and fidelity are obtained.