  This study significantly concentrates on cryogenic InP HEMT high-frequency
circuit analysis using quantum theory to find how the transistor nonlinearity
can affect the quantum correlation of the modes generated in the circuit.
Firstly, the total Hamiltonian of the circuit is derived, and the dynamic
equation of the motion contributed is examined using the Heisenberg-Langevin
equation. Using the nonlinear Hamiltonian, some components are attached to the
intrinsic internal circuit of InP HEMT to fully address the circuit
characteristics. The components attached are arisen due to the nonlinearity
effects. As a result, the theoretical calculations show that the states
generated in the circuit are mixed, and no pure state is produced. Accordingly,
the modified circuit generates the two-mode squeezed thermal state, which means
one can focus on calculating the Gaussian quantum discord to evaluate quantum
correlation. It is also found that the nonlinearity factors (addressed as the
nonlinear components in the circuit) can intensely influence the squeezed
thermal state by which the quantum discord is changed. Finally, as the primary
point, it is concluded that although it is possible to enhance the quantum
correlation between modes by engineering the nonlinear components; however,
quantum discord greater than unity, entangled microwave photons, seems a
challenging task since InP HEMT operates at 4.2 K.
