  Hamiltonian Mechanics works for conserved systems and Quantum Mechanics is
given in Hamiltonian language. It is considered that complexifying the quantum
Hamiltonian, a balanced loss and gain model can be created. The usual
mathematics of density operator formalism and entanglement is extrapolated to
such systems and the consequences are studied. Namely, a complete formalism
using Density operators is created for real eigenvalue regime of these Non-
Hermitian systems and correct forms of Von-Neumann and Entanglement Entropy are
created. The consequences are studied in this regime and depicted w.r.t recent
papers by [9, 20].
