  We suggest the improvement of description methods for quantum phase gate
implementation in the cavity of QED configuration. Qubits are encoded into two
lowest Fock state. Three qubit phase transformation is resulted from the
interaction between Rydberg atom and three modes of cavity electromagnetic
field. Evolution of conditional field states appearing after atom measurement
is described by Kraus transformers. One of these operators is very convenient
for phase gate implementation. We show that it corresponds to conditional
evolution without quantum jumps. Also we describe cavity based generating EPR
pair from certain initially disentangled state.
