Entanglement Evolution of Noisy Quantum Systems: Master Equation-TFD Solutions

Abstract

In this paper, Thermofield Dynamics (TFD) is applied to map a quantum optics nonlinear master equation into a Schrodinger-like equation for any arbitrary initial condition. This formalism provides a more efficient way for solving open quantum system problems. Then we use the Hartree-Fock approximation to solve the master equations of two separate noisy quantum systems analytically, which allows us to analyze the entanglement and quantum mutual information in each case using the eigenvalues of a covariance matrix, followed by two-mode and single-mode squeezed states.

Figures (5)

• Figure 1: Schematic diagram of a coupled two single-mode system exposed to an external field $E(t)$, and $g$ is the coupling distance between them.
• Figure 2: Time evolution of logarithmic negativity $E_n$ with respect to $t$. Here $\gamma_1$ = 0.1, $\mathcal{W}$ = 1.5 and $\Delta$ = 0.1.
• Figure 3: Time evolution of quantum mutual information $I_m$ with respect to $t$. Here, $\gamma_1$ = 0.1, $\mathcal{W}$ = 0.1 and $\Delta$ = 0.1.
• Figure 4: Time evolution of logarithmic negativity $E_n$ with respect to $t$. Here $\gamma_1$ = 0.1, $\mathcal{W}$ = 1.5 and $\Delta$ = 0.1.
• Figure 5: Time evolution of quantum mutual information with respect to $t$. Here $\gamma_1$ = 0.1, $\mathcal{W}$ = 0.1 and $\Delta$ = 0.1.