# Simultaneous Classical Communication and Quantum Key Distribution Based on Plug-and-Play Configuration with an Optical Amplifier

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## Abstract

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## 1. Introduction

## 2. Protocol Description

#### 2.1. The Plug-and-Play DPMCS Protocol

#### 2.2. SCCQ Protocol Based on Plug-and-Play Configuration

#### 2.3. Addition of an Optical Amplifier

## 3. Performance Analysis and Discussion

#### 3.1. Noise Model of SCCQ Protocol Based on Plug-and-Play Configuration

#### 3.2. Simulation Results

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Parameter Optimization

**Figure A1.**SCCQ protocol based on plug-and-play configuration using homodyne detection with a practical detector, d = 50, G = 1.

**Figure A2.**SCCQ protocol based on plug-and-play configuration using homodyne detection with a practical detector, g = 1.005, G = 1.

**Figure A3.**SCCQ protocol based on plug-and-play configuration using homodyne detection with a practical detector, g = 1.005, d = 40.

## Appendix B. Calculation of Asymptotic Secret Key Rate

## Appendix C. Secret Key Rate in the Finite-Size Scenario

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**Figure 1.**The prepared-and-measure scheme of plug-and-play dual-phase modulated coherent states (DPMCS) protocol. (

**a**) Gaussian modulation scheme by using two phase modulators. PIA, phase insensitive amplifier; RNG, random number generator; PM, phase modulator; FM, Faraday mirror.

**Figure 2.**Simultaneous classical communication and quantum key distribution (SCCQ) protocol based on plug-and-play configuration. The probability distributions of X-quadrature measurement is shown at Alice’s side.

**Figure 3.**Schematic diagram of the modified protocol (SCCQ protocol based on plug-and-play configuration with an optical amplifier).

**Figure 4.**The required displacement $\alpha $ as a function of modulation variance ${V}_{B}$ and transmission distance to obtain a BER of ${10}^{-9}$ in the classical channel. Parameters $\gamma =0.2dB/km$, $\eta =0.5$, and ${\upsilon}_{el}=0.1$.

**Figure 5.**Comparison of secret key rate between the modified protocol (homodyne detection with phase-sensitive amplifier (PSA)) and the original protocol (without PSA) under different imperfect source scenarios. Solid lines represent the original protocol (G = 1) while the dashed lines represent the modified protocol (G = 3). From left to right, the green curves correspond to $g=1.015$, the black curves correspond to $g=1.01$, the red curves correspond to $g=1.005$, and the blue curves correspond to $g=1$ (no source noise). The simulation parameters are ${V}_{B}=4$, ${\zeta}_{p}={10}^{-6}$, ${\zeta}_{RB}=0.02$, $\eta =0.5$, ${\upsilon}_{el}=0.1$.

**Figure 6.**Finite-size secret key rate of SCCQ protocol based on plug-and-play configuration with PSA as a function of transmission distance under different imperfect source scenarios. Solid lines represent the original protocol (G = 1) while the dashed lines represent the modified protocol (G = 3). From left to right, the green curves, the black curves, and the red curves correspond to finite-size scenario of block length $N={10}^{6}$, ${10}^{8}$, and ${10}^{10}$, respectively, and the blue curves represent the asymptotic scenario. (

**a**) The parameter $g=1$ (no source noise). (

**b**) The parameter $g=1.005$. (

**c**) The parameter $g=1.01$. (

**d**) The parameter $g=1.015$. Other parameters are set to be the same as Figure 5.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Wu, X.; Wang, Y.; Liao, Q.; Zhong, H.; Guo, Y. Simultaneous Classical Communication and Quantum Key Distribution Based on Plug-and-Play Configuration with an Optical Amplifier. *Entropy* **2019**, *21*, 333.
https://doi.org/10.3390/e21040333

**AMA Style**

Wu X, Wang Y, Liao Q, Zhong H, Guo Y. Simultaneous Classical Communication and Quantum Key Distribution Based on Plug-and-Play Configuration with an Optical Amplifier. *Entropy*. 2019; 21(4):333.
https://doi.org/10.3390/e21040333

**Chicago/Turabian Style**

Wu, Xiaodong, Yijun Wang, Qin Liao, Hai Zhong, and Ying Guo. 2019. "Simultaneous Classical Communication and Quantum Key Distribution Based on Plug-and-Play Configuration with an Optical Amplifier" *Entropy* 21, no. 4: 333.
https://doi.org/10.3390/e21040333