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By using the thermo entangled state representation we solve the masterequation for a dissipative cavity with Kerr medium to obtain density operators'infinite operator-sum representation}$\rho (t)=\sum_{m,n,l=0}^{\infty}M_{m,n,l}\rho_{0}\mathcal{M}_{m,n,l}^{\dagger}.$ It isnoticeable that}$M_{m,n,l}$ is not hermite conjugate to$\mathcal{M}_{m,n,l}^{\dagger}$, nevertheless thenormalization}$\sum_{m,n,l=0}^{\infty}\mathcal{M}_{nm,,l}^{\dagger}M_{m,n,l}=1$still holds}, i.e., they are trace-preserving in a general sense. This examplemay stimulate further studying if general superoperator theory needsmodification.

international journal of theoretical physics

Infinite operator-sum representation of density operator for a  dissipative cavity with Kerr medium derived by virtue of entangled state  representation