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Optical and Quantum Electronics

Evolution of the entanglement, photon statistics and quantum Fisher information of a single qubit parity deformed JCM

S. Abdel‐Khalek, Eied Mahmoud Khalil, Adel Bandar Alruqi, Marwan Althomali

Published Jan 3, 2023• 3 citations
Publisher

Abstract

Abstract In this paper we use the atomic version of the quantum Fisher information to estimate the quantum state of the parity deformed JC-Model (PDJCM) that describing the interaction between a SQ (single qubit) and deformed field has a state like Wigner negative binomial distribution. The nonclassical properties of the field is identified by the evolution of the second-order correlation function. The von Neumann entropy is provided for the nonlocal correlation between the SQ and linear (parity deformed) field. Also, the SQQFI (single qubit quantum Fisher information) or the local QFI, within phase shift estimator is obtained and compared with the von Neumann entropy during the interaction time. We examine the effect of the -deformation parameter and time dependent coupling or qubit speed on the dynamical behavior of the proposed quantities. The results verified that the dynamical behavior of the proposed quantities can be controlled by the qubit speed and -deformation parameter and time dependent coupling or qubit speed parameters.

DOI
10.1007/s11082-022-04365-5

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Abstract In this paper we use the atomic version of the quantum Fisher information to estimate the quantum state of the parity deformed JC-Model (PDJCM) that describing the interaction between a SQ (single qubit) and deformed field has a state like Wigner negative binomial distribution. The nonclassical properties of the field is identified by the evolution of the second-order correlation function. The von Neumann entropy is provided for the nonlocal correlation between the SQ and linear (parity deformed) field. Also, the SQQFI (single qubit quantum Fisher information) or the local QFI, within phase shift estimator is obtained and compared with the von Neumann entropy during the interaction time. We examine the effect of the -deformation parameter and time dependent coupling or qubit speed on the dynamical behavior of the proposed quantities. The results verified that the dynamical behavior of the proposed quantities can be controlled by the qubit speed and -deformation parameter and time dependent coupling or qubit speed parameters.
Abstract This study explores the dynamics of a two two-level atomic system interacting with a parity-deformed field, modeled as a coherent state. By varying the parity deformation parameter and incorporating the effects of intensity-dependent coupling, we examine the time evolution of key quantum phenomena. These include atomic population inversion, von Neumann entropy, concurrence, quantum Fisher information, and the Mandel parameter, where each serves as a critical indicator. Our analysis reveals how the interplay between the deformation parameter and coupling effects governs the quantum dynamics, influencing entanglement, parameter estimation, and statistical properties of the field. These insights contribute to a more comprehensive understanding of how to control and optimize quantum phenomena, highlighting the model’s relevance for quantum information processing technologies.
In this paper, we introduce the parity extension of the harmonic oscillator systems to develop the generalized Tavis-Cummings model (T-CM) based on a specific deformation of the Heisenberg algebra. We present a quantum scheme of a two-qubit system (TQS) interacting with a quantized field that is initially prepared in parity deformed coherent states (PDCSs). The dynamical features of the considered system are explored in the presence of parity deformed parameter (PDP) and time-dependent coupling (t-dc). In particular, we examine the amount of the entanglement formed in the qubit–field and qubit–qubit states. We find that the maximal amount of the entanglement may be occurred periodically during the time evolution. Finally, we investigate the influence of PDP on the Fisher information and the photon statistics of the deformed field with respect to the main parameters of the system.
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.
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.
In this article we estimate the nonlocal correlation between a two qubits and OF (optical field) initially started in the even deformed binomial distribution (EDBS). Explicit forms of the EDBS as the initial states of the RF are presented. We investigate the dynamical and statistical properties of the linear entropy as a quantifier of the correlation and purity of the proposed system. Also, the correlation between the two qubits is quantified by the negativity. Some statistical estimations of the RF are investigated by of Mandel parameter and compared by the two types of correlation The relation between the qubit inversion, two qubits-RF nonlocal correlation, negativity and Mandel parameter is obtained. The effective of Stark shift on the dynamical operators for the RF distribution is examined. The results are shown the a high amount of field-qubit nonlocal is reached for a high value of deformation parameter. Also, the statistical properties of the field is Poissonian or sub-Poissonian photon distribution.
We investigate the speed at which entanglement can be generated by an interaction parameter encoded in a two-qubit Hamiltonian, quantified by the derivative of concurrence with respect to the coupling parameter. For arbitrary pure two-qubit states evolving under a general nonlocal interaction, we derive a bound relating this entanglement speed to the quantum Fisher information (QFI). Specifically, we show that ∣∂gC∣≤FQ(g)1−C2|\partial_g C| \le \sqrt{F_Q^{(g)}} \sqrt{1-C^2}∣∂g​C∣≤FQ(g)​​1−C2​, where FQ(g)F_Q^{(g)}FQ(g)​ is the QFI associated with estimation of the parameter. This establishes FQ1−C2\sqrt{F_Q}\sqrt{1-C^2}FQ​​1−C2​ as an upper bound on the speed of entanglement generation in parameter space. We further derive the saturation conditions and identify the states and dynamical regimes for which equality is attained. At saturation, concurrence evolves at the maximum rate permitted by the distinguishability of the underlying quantum state. These results reveal a direct connection between quantum metrology and entanglement generation, showing that the same information-theoretic quantity that governs parameter-estimation precision also limits the speed at which entanglement resources can be created.