# Correlations in Two-Qubit Systems under Non-Dissipative Decoherence

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Framework

#### 2.1. Quantum Discord

#### 2.2. Generalized Measures of Correlations

#### 2.2.1. Squared Bures Distance

#### 2.2.2. Squared Hellinger Distance

#### 2.2.3. Quantum Jensen–Shannon Divergence

#### 2.3. Two-Qubit States with Maximally Mixed Marginals

## 3. Results

- If $c=|{c}_{1}|$⇒$|{z}_{1}\left({\mathit{s}}_{M}\right)|=1$, ${z}_{2}\left({\mathit{s}}_{M}\right)={z}_{3}\left({\mathit{s}}_{M}\right)=0$;
- If $c=|{c}_{2}|$⇒$|{z}_{2}\left({\mathit{s}}_{M}\right)|=1$, ${z}_{1}\left({\mathit{s}}_{M}\right)={z}_{3}\left({\mathit{s}}_{M}\right)=0$;
- If $c=|{c}_{3}|$⇒$|{z}_{3}\left({\mathit{s}}_{M}\right)|=1$, ${z}_{2}\left({\mathit{s}}_{M}\right)={z}_{1}\left({\mathit{s}}_{M}\right)=0$.

#### Behavior of Correlations under Non-Dissipative Decoherence

**Example**

**1.**

**Example**

**2.**

**Example**

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## 4. Concluding Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Dynamics of the generalized total correlation measures as a function of $\gamma t$ for ${c}_{1}\left(0\right)=0.8$, ${c}_{2}\left(0\right)=-{c}_{3}\left(0\right)$, ${c}_{3}\left(0\right)=0.6$.

**Figure 2.**Dynamics of the generalized classical correlation measures as a function of $\gamma t$ for ${c}_{1}\left(0\right)=0.8$, ${c}_{2}\left(0\right)=-{c}_{3}\left(0\right)$, ${c}_{3}\left(0\right)=0.6$.

**Figure 3.**Dynamics of the generalized quantum correlation measures as a function of $\gamma t$ for ${c}_{1}\left(0\right)=0.8$, ${c}_{2}\left(0\right)=-{c}_{3}\left(0\right)$, ${c}_{3}\left(0\right)=0.6$.

**Figure 4.**Dynamics of the generalized quantum correlation measures for the quantum Jensen–Shannon divergence, as a function of $\gamma t$, considering the initial conditions of the freezing phenomenon of quantum discord: ${c}_{1}\left(0\right)=0.8$, ${c}_{2}\left(0\right)=-{c}_{1}\left(0\right){c}_{3}\left(0\right)$, ${c}_{3}\left(0\right)=0.6$. ${t}^{\ast}\approx 0.144$.

**Figure 5.**Dynamics of the generalized quantum correlation measures for the squared Bures distance case, as a function of $\gamma t$, considering the initial conditions of the freezing phenomenon of quantum discord: ${c}_{1}\left(0\right)=0.8$, ${c}_{2}\left(0\right)=-{c}_{1}\left(0\right){c}_{3}\left(0\right)$, ${c}_{3}\left(0\right)=0.6$. ${t}^{\ast}\approx 0.144$.

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**MDPI and ACS Style**

Bussandri, D.G.; Osán, T.M.; Lamberti, P.W.; Majtey, A.P. Correlations in Two-Qubit Systems under Non-Dissipative Decoherence. *Axioms* **2020**, *9*, 20.
https://doi.org/10.3390/axioms9010020

**AMA Style**

Bussandri DG, Osán TM, Lamberti PW, Majtey AP. Correlations in Two-Qubit Systems under Non-Dissipative Decoherence. *Axioms*. 2020; 9(1):20.
https://doi.org/10.3390/axioms9010020

**Chicago/Turabian Style**

Bussandri, Diego G., Tristán M. Osán, Pedro W. Lamberti, and Ana P. Majtey. 2020. "Correlations in Two-Qubit Systems under Non-Dissipative Decoherence" *Axioms* 9, no. 1: 20.
https://doi.org/10.3390/axioms9010020