Question

hello, I need a clear and sufficient definition with the references for:
1- Wehrl entropy.
2-Mandel parameter.
3-Atomic fisher information.
4-Quantum fisher information.

Answer 1

Wehrl entropy

1)In quantum information theory, the Wehrl entropy, named after Alfred Wehrl, is a classical entropy of a quantum-mechanical density matrix. It is a type of quasi- entropy defined for the Husimi Q representation of the phase-space quasiprobability distribution.

2)The Mandel Q parameter measures the departure of the occupation number distribution from Poissonian statistics. It was introduced in quantum optics by L. Mandel. It is a convenient way to characterize non-classical states with negative values indicating a sub-Poissonian statistics, which have no classical analog.

3) statistical model for forecasting the quantum entanglement between a two‐qubit and optical field in binomial distribution. We explore the link between the atomic Fisher information, quantum entropy, and the statistical properties of the field. The qubit‐qubit entanglement is investigated through concurrence during the interaction time. The dynamics of the statistical quantities will be forecasted using the time series and neural network models. The effect of the field distribution parameter (number of successes) is examined by the time series models and artificial neural network. We compare the accuracy of both modes from the perspective of the dynamic of the quantum entropy and atomic Fisher information. A statistical description for the data has been obtained and is discussed to show the statistical technique analysis the data of statistical quantities. The results obtained have several applications and are related with quantum statistics and quantum information processing.

4)The quantum Fisher information of an atomic system interacting with a single cavity mode in the presence of Kerr medium is discussed. It is shown that quantum Fisher information for an initial separable atomic system is larger than that depicted for the initial entangled atomic system.

it is shown that the Thomas–Fermi Fisher information is negative. A slightly more sophisticated model proposed by Gaspar provides a qualitatively correct expression for the Fisher information: Gaspar’s Fisher information is proportional to the two-third power of the atomic number. Accurate numerical calculations show an almost linear dependence on the atomic number.

For initial vacuum state of the cavity mode, the quantum Fisher information with respect to the Kerr medium and the phase decoherence parameter is larger than that displayed for the detuning parameter. Both phase decoherence and Kerr medium have the same effect on the decay of quantum Fisher information, while they have an opposite effect on its maximum values.