In this contribution we study a
superposition of two finite dimensional trio coherent states (FTCS). The state
is regarded as a correlated three-mode state in finite dimensional bases. The
framework of Pegg and Barnett formalism, and the phase distribution in addition to the Poissonian
distribution are examined. It is shown that the eigenvalue of the difference of
the photon number (the q-parameter)
is responsible for the non-classical phenomenon. Furthermore, the
quasi-probability distribution functions (the Wigner and Q-functions) are also discussed. In this case and for the Wigner
function the non-classical behavior is only reported for the odd values of the q-parameter.
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