Fisher Information and Statistical Properties of Two Qubits in Two Modes of the Gaussian Distribution

Abstract

We estimate the quantum state of two qubits and a two-mode field obeying the Gaussian distribution and give the two Gaussian modes and the density matrix in explicit forms. We study the dynamic properties of the Mandel parameter as a quantifier of the statistical properties for the radiation field during the process of its time evolution. We investigate the nonlocal correlation between the two atoms as well as their entanglement with the field distribution. In addition, we obtain the Fisher information based on the estimation of the atomic state and compare it with the Mandel parameter. Finally, we explore the link between the statistical quantities of the field for different parameters of the two Gaussian modes.