# Entanglement of General Two-Qubit States in a Realistic Framework

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Entanglement of an Arbitrary State of a System of Two Qubits

## 3. More General Non-Orthogonal States of Two Qubits in the Context of SCSs

- (1)
- ${\alpha}_{i}={\alpha}_{i}^{{}^{\prime}}$, which displays a mixed state with zero entanglement ($C\left(\rho \right)=0$).
- (2)
- ${\alpha}_{i}=-1/{\alpha}_{i}^{{}^{\prime}}$, which corresponds to a mixed state defined as a statistical mixture of a maximally entangled state and a separable state with concurrence ${C}^{2}\left(\rho \right)={p}_{i}^{2}.$

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The variation of the concurrence of the state $|\Psi \rangle $ in terms of $\alpha $ with various values of ${\alpha}^{{}^{\prime}}$ for $a=b=1/2$. The maximum is attained for $\alpha {\alpha}^{{}^{\prime}}=-1$.

**Figure 2.**The variation of the concurrence of the state $|\Psi \rangle $ in terms of $\alpha $ with various values of ${\alpha}^{{}^{\prime}}$ for $a=4/7$ and $b=3/7$. The maximum is attained for $\alpha {\alpha}^{{}^{\prime}}=-1$.

**Figure 3.**The variation of the concurrence of the state $\rho $ in terms of ${\alpha}_{i}$ and ${\alpha}_{i}^{{}^{\prime}}$ for ${p}_{i}=1/2$ and ${a}_{i}={b}_{i}=1/2$.

**Figure 4.**The variation of the concurrence of the state $\rho $ in terms of ${\alpha}_{i}$ and ${\alpha}_{i}^{{}^{\prime}}$ for ${p}_{i}=8/10$ and ${a}_{i}={b}_{i}=1/2$.

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**MDPI and ACS Style**

Abdel-Khalek, S.; Berrada, K.; Khalil, E.M.; Almalki, F.
Entanglement of General Two-Qubit States in a Realistic Framework. *Symmetry* **2021**, *13*, 386.
https://doi.org/10.3390/sym13030386

**AMA Style**

Abdel-Khalek S, Berrada K, Khalil EM, Almalki F.
Entanglement of General Two-Qubit States in a Realistic Framework. *Symmetry*. 2021; 13(3):386.
https://doi.org/10.3390/sym13030386

**Chicago/Turabian Style**

Abdel-Khalek, Sayed, Kamal Berrada, Eied M. Khalil, and Fadhel Almalki.
2021. "Entanglement of General Two-Qubit States in a Realistic Framework" *Symmetry* 13, no. 3: 386.
https://doi.org/10.3390/sym13030386