  The quantum correlation between microwave modes in an RF electronic circuit
is analyzed and studied. An open quantum system operating at 4.2 K is designed
in which InP HEMT as the nonlinear component couples two external oscillators
to each other. The quantum theory is applied to completely analyze the system,
by which the related quantum Hamiltonian containing all noise sources is
derived. The Lindblad Master equation is used to analyze the time evolution of
the expanded closed system that covers the environmental effects. In the
following, the state of the system defined is determined in terms of the
ensemble average state using the density matrix; then, the ensemble average of
the different operators is calculated. Accordingly, the covariance matrix of
the quantum system is derived, and the quantum discord as a key quantity to
determine the quantum correlation is calculated. As an interesting point, the
results show that InP HEMT mixes two coupling oscillator modes so that the
quantum correlation is created at different frequency productions such as 2nd,
3rd, and 5th. The harmonics suitable for sampling and digitalization is the
zero-IF (downside of 2nd harmonics) band at which the quantum correlation is
generated. Another point is that there is no quantum correlation at the
frequency resonance of each oscillator coupled to InP HEMT.
