# Enhanced Superdense Coding over Correlated Amplitude Damping Channel

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## Abstract

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## 1. Introduction

## 2. Superdense Coding under the CAD Channel

## 3. Enhanced Superdense Coding under CAD Channel

#### 3.1. WM+CAD+QMR Scheme

#### 3.2. CAD+EAM+QMR Scheme

## 4. Comparison between WM+CAD+QMR Scheme and CAD+EAM+QMR Scheme

## 5. Discussions and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(color online) The capacity ${C}_{\mathrm{CAD}}^{\ast}$ of superdense coding as a function of the correlation parameter $\mu $ and the decoherence strength $\gamma $. The blank regions indicate the quantum advantage of superdense coding has disappeared. CAD: correlated amplitude damping.

**Figure 2.**(color online) The capacity improvement ${C}_{\mathrm{imp}}^{1}$ as a function of the correlated parameter $\mu $ and the decoherence strength $\gamma $. From left to right, the strengths of WM $p=0.1$ (

**a**), $p=0.5$ (

**b**) and $p=0.9$ (

**c**), respectively. The parameter q is set to $q=p+\gamma \overline{p}$.

**Figure 3.**(color online) The successful probability of weak measurement (WM)+CAD+quantum measurement reversal (QMR) scheme ${P}_{\mathrm{WM}}^{\ast}$ as a function of the strength of decoherence $\gamma $ for different correlated parameters $\mu $. From left to right, the strengths of WM are $p=0.1$ (

**a**), $p=0.5$ (

**b**) and $p=0.9$ (

**c**), respectively. The parameter q is set to $q=p+\gamma \overline{p}$.

**Figure 4.**(color online) The capacity difference ${C}_{\mathrm{imp}}^{2}$ between ${C}_{\mathrm{EAM}}^{\ast}$ and ${C}_{\mathrm{CAD}}^{\ast}$ as a function of the memory parameter $\mu $ and the decoherence strength $\gamma $. EAM: environment-assisted measurement.

**Figure 5.**(color online) The successful probability of EAM+QMR scheme ${P}_{\mathrm{EAM}}^{\ast}$ as a function of the strength of decoherence $\gamma $ for different memory parameters $\mu $.

**Figure 6.**(color online) The capacity difference ${C}_{\mathrm{imp}}^{3}$ between ${C}_{\mathrm{EAM}}^{\ast}$ and ${C}_{\mathrm{WM}}^{\ast}$ as a function of $\mu $ and $\gamma $ with $p=0.1\left(\mathbf{a}\right),0.5\left(\mathbf{b}\right),0.9\left(\mathbf{c}\right)$ in turn.

**Figure 7.**(color online) The ratio ${P}_{\mathrm{EAM}}^{\ast}/{P}_{\mathrm{WM}}^{\ast}$ as a function of $\gamma $ for different $\mu $ when $p=0.1\left(\mathbf{a}\right),0.5\left(\mathbf{b}\right),0.9\left(\mathbf{c}\right)$, one after another.

**Figure 8.**(color online) Average capacity $D={C}^{\ast}\ast {P}^{\ast}$ as a function of the decoherence strength $\gamma $ with $\mu =0.1$, $p=0$.

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**MDPI and ACS Style**

Li, Y.-L.; Wei, D.-M.; Zu, C.-J.; Xiao, X.
Enhanced Superdense Coding over Correlated Amplitude Damping Channel. *Entropy* **2019**, *21*, 598.
https://doi.org/10.3390/e21060598

**AMA Style**

Li Y-L, Wei D-M, Zu C-J, Xiao X.
Enhanced Superdense Coding over Correlated Amplitude Damping Channel. *Entropy*. 2019; 21(6):598.
https://doi.org/10.3390/e21060598

**Chicago/Turabian Style**

Li, Yan-Ling, Dong-Mei Wei, Chuan-Jin Zu, and Xing Xiao.
2019. "Enhanced Superdense Coding over Correlated Amplitude Damping Channel" *Entropy* 21, no. 6: 598.
https://doi.org/10.3390/e21060598