# Quantum Fisher Information and Bures Distance Correlations of Coupled Two Charge-Qubits Inside a Coherent Cavity with the Intrinsic Decoherence

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## Abstract

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## 1. Introduction

## 2. Time Evolution of the Physical Model

## 3. Quantum Fisher Information and Bures Distance Entanglement

#### 3.1. Local Quantum Fisher Information

#### 3.2. Bures Distance Entanglement

## 4. Dynamics of the Correlation Quantifiers

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic diagram of two identical coupled charge qubits with coupling strength K, are placed in a single-mode SC-cavity. Each qubit is characterized by a junction capacitance ${C}_{J}$ and a coupling energy ${E}_{J}$ which is tuned by applying a ${\mathsf{\Phi}}_{c}$ to the Cooper-pair box that containing two identical Josephson junctions with the coupling energies ${E}_{J}$ and capacitors ${C}_{J}$.

**Figure 2.**The local quantum Fisher information $L\left(t\right)$ (solid curve) and Bures distance entanglement $B\left(t\right)$ (dashed curve) for $\mu =2\sqrt{2}$, $\gamma =0.0$, $r=0$ for different two-qubit coupling values: $K/\lambda =0.0$ in (

**a**) and $K/\lambda =20$ in (

**b**).

**Figure 4.**As Figure 2, but when the cavity is initially in the even coherent state.

LQFI | BDE | The Observations | Figs. | |
---|---|---|---|---|

OF | Yes | Yes | OF of $L\left(t\right)$ is more than of $B\left(t\right)$ | Figure 2 and Figure 4 |

OA | Yes | Yes | OA of $L\left(t\right)$ are larger than of $B\left(t\right)$ | All |

SD | No | Yes | SD is only in $B\left(t\right)$ | Figure 4a and Figure 5a |

SC | Yes | No | SC are only in $L\left(t\right)$ | Figure 5b |

FC | Yes | No | FC is only in $L\left(t\right)$ | Figure 2b, Figure 3b and Figure 5b |

SC | Yes | Yes | SC of $L\left(t\right)$ is more than of $B\left(t\right)$ | Figure 3a and Figure 5a |

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**MDPI and ACS Style**

Mohamed, A.-B.A.; Khalil, E.M.; Selim, M.M.; Eleuch, H.
Quantum Fisher Information and Bures Distance Correlations of Coupled Two Charge-Qubits Inside a Coherent Cavity with the Intrinsic Decoherence. *Symmetry* **2021**, *13*, 352.
https://doi.org/10.3390/sym13020352

**AMA Style**

Mohamed A-BA, Khalil EM, Selim MM, Eleuch H.
Quantum Fisher Information and Bures Distance Correlations of Coupled Two Charge-Qubits Inside a Coherent Cavity with the Intrinsic Decoherence. *Symmetry*. 2021; 13(2):352.
https://doi.org/10.3390/sym13020352

**Chicago/Turabian Style**

Mohamed, Abdel-Baset A., Eied. M. Khalil, Mahmoud M. Selim, and Hichem Eleuch.
2021. "Quantum Fisher Information and Bures Distance Correlations of Coupled Two Charge-Qubits Inside a Coherent Cavity with the Intrinsic Decoherence" *Symmetry* 13, no. 2: 352.
https://doi.org/10.3390/sym13020352