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International Journal of Quantum Chemistry

Atomic Fisher information and entanglement forecasting for quantum system based on artificial neural network and time series model

S. Abdel‐Khalek, Azhri Alhag, Mahmoud Ragab, Sayed Mohamed Abo-Dahab, Ali Algarni, Hijaz Ahmad

Published Sep 9, 2020• 6 citations
Publisher

Abstract

Abstract In this article, we apply a 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.

DOI
10.1002/qua.26446

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In this paper, a quantum scheme for a two-qubit system (2QS) and field initially prepared in the excited negative binomial distribution is presented. The field photon statistics is detected from the evolution of the Mandel parameter, while the evolution of von Neumann entropy detects the nonlocal correlation between the 2QS and radiation field. The concurrence is used to detect the qubit-qubit entanglement during the time evolution. The dynamical properties of single-qubit and two-qubit quantum Fisher information are investigated. We visualize the number of photon excitations on the field in negative binomial states with influence of photon success probability. A connection is provided between the dynamical behaviors of these statistical quantities. We have found that the proposed quantities are strongly influenced by the number of excited photons of the field in negative binomial states and photon success probability.
We developed a quantum scheme of two atoms (TAs) and field initially in a negative binomial state (NBS). We displayed and discussed the physical implications of the obtained results in terms of the physical parameters of the model. By considering that the TAs were initially prepared in a maximally entangled state, and that the single-mode field was in the NBS, the dynamics of quantum phenomena such TAs-field entanglement, TAs entanglement, and parameter estimation were examined. We found that the quantum quantifiers exhibited randomly quasi-periodic and periodic oscillations that depended on the success probability, photon number transition, and the intensity-dependent coupling effect. Furthermore, we analyzed the connection between the dynamical behavior of the quantifiers. This system can be compared with some other ones that are being discussed in the literature, in order to realize the quantum entanglement, and to control the precision of the parameter estimation.
We consider a quantum system of an atom-atom interaction in the presence of two external magnetic and classical fields in x, and z directions. The dynamical behavior of single atom quantum quantifiers such as the atomic Wehrl entropy, atomic Fisher information and quantum entropy are investigated. The quantum entanglement degradation in regard to the atomic state estimation are discussed through the evolution of the atomic Fisher information flow, and the effects of the external classical fields and types of time dependent coupling between the two atoms are examined. We explore the relationship between different statistical quantities in the absence and presence of classical field during the time evolution. The results show that the creation and manipulation of entanglement by external fields greatly benefit within the suitable choice of the kind of time dependent coupling among the two atoms and external.
A statistical method is applied to predict the behaviour of a quantum model consisting of a qubit interacting with a single-mode cavity field. The qubit is prepared in excited state while the field starts from the binomial distribution state. The wave function of the proposed model is obtained. A von Neumann entropy is used to investigate the behaviour of the entanglement between the field and the qubits. Moreover, the atomic Q and Wigner functions are used to identify the behaviour of the distribution in a phase space. The simulation method is used to estimate the parameters of the proposed model to reach the best results. A numerical study is performed to estimate the specific dependency of the binomial distribution state. The results of entanglement were compared with the atomic Q and Wigner functions. The results showed that there are many maximum values of entanglement periodically. The results also confirmed a correlation between von Neumann entropy, the atomic Q , and Wigner functions.