# High-Performance Intermediate-Frequency Balanced Homodyne Detector for Local Local Oscillator Continuous-Variable Quantum Key Distribution

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## Abstract

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## 1. Introduction

## 2. Local Local Oscillator CV-QKD Scheme

## 3. High-Performance Intermediate-Frequency BHD

#### 3.1. Circuit Design

#### 3.2. Bandwidth and QCNR

#### 3.3. Linearity and Gain

## 4. System Performance with Intermediate-Frequency BHD

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Diagram of the simplified local local oscillator CV-QKD architecture. AM: amplitude modulator, PM: phase modulator, BS: beam splitter, VOA: variable optical attenuator, DPC: dynamic polarization controller, PD: photodiode, TIA: trans-impedance amplifier, LO frequency: the local oscillator frequency of the mixer, ADC: analog-to-digital converter.

**Figure 2.**Simplified electronic circuit schematic of the intermediate-frequency BHD. V+: positive supply voltage, V-: negative supply voltage, PD: photodiode, ADL5523: ratio frequency amplification chip, JMS: frequency mixer chip, LPF: low-pass filter.

**Figure 3.**Diagram of the optical experiment. The red lines are optical paths, and the black lines are electrical paths. Laser: 1550 nm continuous-wave fiber laser, AWG: arbitrary waveform generator, VOA: variable optical attenuators, VOD: variable optical delay, AM: amplitude modulator, BS: beam splitter, PD: photodiode, LO: local oscillator, LPF: low pass filter.

**Figure 4.**(

**a**) Measured noise power of intermediate-frequency BHD without a mixer ranging from kHz to 1.5 GHz. BHD noise spectrum at CW LO powers of 0.5, 1, 2, 3, 4, 5, 7, 9 mW (from the third lowest to highest curve). Bg noise: Spectrum analyzer background noise spectrum, Ele noise: BHD electronic noise spectrum, resolution bandwidth: 100 kHz. (

**b**) Measured noise power of intermediate-frequency BHD with mixer and LPF. Intermediate-frequency BHD noise spectrum at CW LO powers of 0.5, 1, 2, 3, 4, 5, 7, 9 mW (from the third lowest to highest curve). LPF: DC-270 MHz. Resolution bandwidth: 100 kHz.

**Figure 5.**(

**a**) Noise variance as a function of the CW LO power in the time domain. The red curve is the total noise composed of electronic noise and quantum noise. The black line is electronic noise from the BHD and other instruments. The green curve is quantum noise obtained by subtracting the electronic noise from the total noise. The quantum noise variance to the electronic noise variance ratio is 15.0 dB at a LO power of 9 mW. (

**b**) Intermediate-frequency BHD output voltage as a function of the optical power. The “PD+” and “PD−” are reversely biased photodiodes to generate the opposite current. The black squares are the output voltage when only “PD+” is illuminated, and the red triangles are the output voltages when only “PD−” is illuminated. The black line represents the fitting line of the output voltage.

**Figure 6.**Secure key rate as a function of the transmission distance-based intermediate-frequency BHD. The blue curves from left to right represent the achievable key rate considering the finite-size effect with $N={10}^{8}$, $N={10}^{9}$, and the asymptotic effect. Besides, the black curve corresponds to the PLOB bound [38,39]. Other parameters in our results are as follows: the modulation variance ${V}_{A}=3$, the electronic noise ${v}_{el}=0.0384$, the detection efficiency $\eta =0.612$, the loss coefficient of optical fiber $\alpha $ = 0.2 dB/km, and the excess noise $\epsilon =0.05$.

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**MDPI and ACS Style**

Qi, D.; Wang, X.; Chen, Z.; Lu, Y.; Yu, S.
High-Performance Intermediate-Frequency Balanced Homodyne Detector for Local Local Oscillator Continuous-Variable Quantum Key Distribution. *Symmetry* **2023**, *15*, 1314.
https://doi.org/10.3390/sym15071314

**AMA Style**

Qi D, Wang X, Chen Z, Lu Y, Yu S.
High-Performance Intermediate-Frequency Balanced Homodyne Detector for Local Local Oscillator Continuous-Variable Quantum Key Distribution. *Symmetry*. 2023; 15(7):1314.
https://doi.org/10.3390/sym15071314

**Chicago/Turabian Style**

Qi, Dengke, Xiangyu Wang, Ziyang Chen, Yueming Lu, and Song Yu.
2023. "High-Performance Intermediate-Frequency Balanced Homodyne Detector for Local Local Oscillator Continuous-Variable Quantum Key Distribution" *Symmetry* 15, no. 7: 1314.
https://doi.org/10.3390/sym15071314