Quantum Extropy and Statistical Properties of the Radiation Field for Photonic Binomial and Even Binomial Distributions

Abstract

We present quantum formula for extropy based on the Husimi Q-function and the atomic Husimi Q-function. The quantum extropy is used to detect the entanglement or nonlocal correlations of the system consisted of a single qubit and the radiation field. We provide explicit forms of the binomial and even binomial distributions. We compare the temporal behavior of quantum extropy within the atomic and field bases with the tomographic entropy, which is a measure for quantifying nonlocal correlations between the field and a single qubit. The photon statistics of the field can also be quantified by the evolution of the Mandel parameter, if the field initially follows the binomial and even binomial distributions. We use the total density matrix to compute and analyze the time evolution of the initial photonic binomial probability distribution that governs the behavior of the atom–photon entanglement. In this context, we investigate the links among the temporal behavior of the atomic quantum extropy, tomographic entropy, and statistical properties of the field. The quantum extropy is a useful indicator of the qubit–field entanglement, whereas the quantum extropy of the field basis is a good indicator of the dynamical behavior of the atom–field system.