Quantum operational measurement of amplitude and phase parameters for SU(3) symmetry optical fields

We consider a new approach for describing a quantum optical Bose system with internal Gell-Mann symmetry by means of the SU(3) symmetry polarization map in Hilbert space. The operational measurement of the density (or coherency) matrix elements for the three-mode optical field is discussed for the first time. We have introduced a set of operators that describe the quantum measurement procedure and the behaviour of fluctuations for the amplitude and phase characteristics of the three-level system. A novel twelve-port interferometer for making parallel measurements of the Gell-Mann parameters is proposed. The quantum properties of qutrit W-states in the measurement procedure are examined.