# Multiplexing Quantum and Classical Channels of a Quantum Key Distribution (QKD) System by Using the Attenuation Method

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State of the Art

## 3. Quantum Channel Positioning

## 4. Methods of Quantum Multiplexing

**Large spacing method**—Commonly used by QKD system manufacturers. It is based on the largest possible spacing between quantum and classical channels (while respecting suitable wavelengths in the fiber). Typically, quantum channels are placed in the O-band (1310 nm), and classical channels are placed in the C-band (1550 nm). The total spacing is thus approximately 240 nm, and thus, Raman noise has minimal effect on the quantum channel. Such a technique is simple to implement and is described with an example of a possible metropolitan network in [29].**Narrow filtering method**—Procedure described in [30]. Both types of channels are located in the C-band in relative proximity. Most of the Raman noise is filtered out by using the narrowest possible filters (DWDM 50 GHz, 25 GHz, 12.5 GHz).**Attenuation method**—Our method, which is described in detail in this article. Like the second one, the quantum and service channels are positioned close to each other. Here, however, conventional 100 GHz filters are used for filtering. For this reason, it is thus necessary to attenuate the other classical channels as much as possible. This also reduces the Raman noise power.

## 5. Attenuation Method Experiment

**Design and safety verification of the initial route**—In this phase, a potentially functional QKD polygon with a route length of 20 km was designed. The length of the fiber was sufficient to manifest nonlinear effects while not exceeding the maximum possible quantum channel attenuation. DWDM filters were used to merge the quantum and classical channels, and their properties were tested by using an optical spectrum analyzer (OSA). Based on the results, these filters were then incorporated at a suitable location in the scheme. The optical power of the originally used Small Form-factor Pluggable (SFP) modules and the attenuation of all the optical elements used were also measured. Based on the calculations, it was verified that there could be no damage to any detection devices in the topology, especially the quantum signal detectors.**Attenuation of service channels**—The second phase consisted of finding the minimum attenuation of the service channels so that the quantum channel was still functional. Testing was performed by using two pairs of SFPs. The first pair was used only for testing, i.e., no useful signal was sent, and the second pair provided a direct service channel link. This was the only way to ensure the correct operation of the entire system.**Building the final route and tuning**—The final step was to build and test a fully functional QKD polygon. Unlike the previous phase, attention was already paid to the service channels, which are also a limiting element when sufficiently attenuated. For this reason, several modifications were made to the route. In particular, the replacement of lossy multiplexers by more attenuation-friendly circulators or the addition of an EDFA at the end of both service channels was carried out. The functionality of this route was tested for distances of 0, 5, 10, 15 and 20 km.

#### 5.1. Phase I: Design and Safety Verification of the Iinitial Route

**I. Position**—The main function of the filter is to bind CH30 to a common fiber with a quantum channel and simultaneously extract CH29 from the fiber. Its secondary function is similar to that of the multiplexers described above, that is, to filter out the noise produced by CH30 in the CH32 region. Most of the noise that passes through the MUX is passed to the PASS port, where it is then absorbed by the isolator along with the remnants of CH29.**II. Position**—As in the previous case, the main function of the filter is to bind and unbind the service channels to a common fiber. In this case, however, it is no longer appropriate for the filter to pass the noise of service channel B. Unlike Filter I, most of the noise in the CH32 region must be reflected toward Alice, where it again passes to the isolator and is absorbed.**III. Position**—The filter is mainly used to increase the OSNR (optical signal-to-noise ratio) of the quantum channel. Therefore, its isolation in the COM-PASS direction is important. Service channel residues that are not suppressed by the previous filter are removed from the fiber by the REF port.

#### 5.2. Phase II: Attenuation of Service Channels

#### 5.2.1. Crosstalk or Raman Noise?

#### 5.2.2. Raman Noise Estimation

- Raman noise power generated in the forward direction (→):$$\begin{array}{c}\hfill {P}_{\overrightarrow{SpRS}}={P}_{in}\xb7{e}^{-A}\xb7\rho \left(\lambda \right)\xb7L\xb7\Delta \lambda \end{array}.$$
- Raman noise power generated in the backward direction (←):$$\begin{array}{c}\hfill {P}_{\overleftarrow{SpRS}}={P}_{in}\xb7{e}^{-A}\xb7\rho \left(\lambda \right)\xb7\frac{sinh\left(L\alpha \right)}{\alpha}\xb7\Delta \lambda \end{array}.$$

**Output power**—${P}_{out}$—optical power of the service channel (both have the same value) entering the first DWDM filter. This power must be converted to mW. It can be calculated as ${P}_{out}={P}_{in}\xb7{e}^{-A}={P}_{in}\xb7{e}^{-\alpha \xb7L}$, where A denotes the attenuation.$${P}_{out|+0\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}\phantom{\rule{4.pt}{0ex}}}=-31.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{dBm}=7.08\xb7{10}^{-4}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mW},$$$${P}_{out|+20\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}}=-51.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{dBm}=7.08\xb7{10}^{-6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mW}.$$**Raman scattering coefficient**—$\rho \left(\lambda \right)$—determined from the Raman cross-section graph in [27] for channels two and three positions away from the quantum channel in the Stokes scattering region.$$\rho \left(\lambda \right)=1.85\xb7{10}^{-9}\phantom{\rule{3.33333pt}{0ex}}\frac{1}{\mathrm{km}\xb7\mathrm{nm}}.$$**Bandwidth**—$\Delta \lambda $—the region of the spectrum in which the Raman scattering power is measured. The DWDM channel has a width of 100 GHz, which must be converted to nanometers.$$\Delta \lambda =0.8\phantom{\rule{3.33333pt}{0ex}}\mathrm{nm}\approx \Delta \nu =100\phantom{\rule{3.33333pt}{0ex}}\mathrm{GHz}.$$**Route length**—L—the part of the route where Raman scattering and other nonlinear effects occur.$$L=20\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}.$$**Attenuation coefficient**—$\alpha $—calculated based on the difference between input and output optical power, and then converted to ${\mathrm{km}}^{-1}$.$$\alpha =0.3\phantom{\rule{3.33333pt}{0ex}}\frac{\mathrm{dB}}{\mathrm{km}}=6.91\xb7{10}^{-2}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{km}}^{-1}.$$

**Minimum attenuation (+0 dB)**- -
- ${P}_{\overrightarrow{SpRS|30}}=-106.79\phantom{\rule{3.33333pt}{0ex}}\mathrm{dBm},$
- -
- ${P}_{\overleftarrow{SpRS|29}}=-105.48\phantom{\rule{3.33333pt}{0ex}}\mathrm{dBm},$
- -
- ${P}_{SpRS|QKD}=-103.08\phantom{\rule{3.33333pt}{0ex}}\mathrm{dBm}.$

**Maximum attenuation (+20 dB)**- -
- ${P}_{\overrightarrow{SpRS|30}}=-126.79\phantom{\rule{3.33333pt}{0ex}}\mathrm{dBm},$
- -
- ${P}_{\overleftarrow{SpRS|29}}=-125.48\phantom{\rule{3.33333pt}{0ex}}\mathrm{dBm},$
- -
- ${P}_{SpRS|QKD}=-123.08\phantom{\rule{3.33333pt}{0ex}}\mathrm{dBm}.$

#### 5.3. Phase III: Building the Final Route and Tuning

#### Reducing the Route Length

## 6. Discussion of the Results

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

COW | Coherent One-way |

CV-QKD | Continuous-variable QKD |

CWDM | Coarse WDM |

DTU | Technical University of Denmark |

DV-QKD | Discrete-variable QKD |

DWDM | Dense WDM |

EDFA | Erbium-Doped Fiber Amplifier |

FWM | Four-Wave Mixing |

IDQ | ID Quantique |

ITU-T | International Telecommunication Union—Telecommunication Standardization Sector |

MDI-QKD | Measurement-device Independent QKD |

MUX | Multiplexer |

OSA | Optical Spectrum Analyzer |

OSNR | Optical Signal-to-noise Ratio |

PQC | Postquantum Cryptography |

QBER | Quantum-bit Error Rate |

QKD | Quantum Key Distribution |

QMUX | Quantum Multiplexing |

QRNG | Quantum Random Number Generation |

SFP | Small Form-factor Pluggable |

SpRS | Spontaneous Raman Scattering |

TF-QKD | Twin-field QKD |

VOA | Variable Optical Attenuator |

WDM | Wavelength-division Multiplexing |

## References

- Lovic, V. Quantum Key Distribution: Advantages, Challenges and Policy. Camb. J. Sci. Policy
**2020**, 1. [Google Scholar] [CrossRef] - Peters, N.A.; Toliver, P.; Chapuran, T.E.; Runser, R.J.; McNown, S.R.; Peterson, C.G.; Rosenberg, D.; Dallmann, N.; Hughes, R.J.; McCabe, K.P.; et al. Dense wavelength multiplexing of 1550-nm QKD with strong classical channels in reconfigurable networking environments. New J. Phys.
**2009**, 11, 045012. [Google Scholar] [CrossRef] - Chen, Y.-A.; Zhang, Q.; Chen, T.-Y.; Cai, W.-Q.; Liao, S.-K.; Zhang, J.; Chen, K.; Yin, J.; Ren, J.-G.; Chen, Z.; et al. An integrated space-to-ground quantum communication network over 4600 kilometres. Nature
**2021**, 589, 214–219. [Google Scholar] [CrossRef] [PubMed] - Karen, K. China Reaches New Milestone in Space-Based Quantum Communications. Scientific American. Available online: https://www.scientificamerican.com/article/china-reaches-new-milestone-in-space-based-quantum-communications/ (accessed on 7 September 2023).
- Eagle-1. European Space Agency. Available online: https://www.esa.int/Applications/Connectivity_and_Secure_Communications/Eagle-1 (accessed on 7 September 2023).
- Toshiba Achieves Chip-Based QKD Tech. Photonics Media. 2021. Available online: https://www.bit.ly/3LeOyOv (accessed on 24 August 2023).
- Sibson, P.; Erven, C.; Godfrey, M.; Miki, S.; Yamashita, T.; Fujiwara, M.; Sasaki, M.; Terai, H.; Tanner, M.G.; Natarajan, C.M.; et al. Chip-based quantum key distribution. Nat. Commun.
**2017**, 8, 13984. [Google Scholar] [CrossRef] [PubMed] - Paraïso, T.K.; Roger, T.; Marangon, D.G.; Marco, I.D.; Sanzaro, M.; Woodward, R.I.; Dynes, J.F.; Yuan, Z.; Shields, A.J. A photonic integrated quantum secure communication system. Nat. Photonics
**2021**, 15, 850–856. [Google Scholar] [CrossRef] - KETS. Available online: https://kets-quantum.com (accessed on 7 September 2023).
- Gehring, T.; Händchen, V.; Duhme, J.; Furrer, F.; Franz, T.; Pacher, C.; Werner, R.F.; Schnabel, R. Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks. Nat. Commun.
**2015**, 6, 8795. [Google Scholar] [CrossRef] [PubMed] - Eriksson, T.A.; Hirano, T.; Puttnam, B.J.; Rademacher, G.; Luís, R.S.; Fujiwara, M.; Namiki, R.; Awaji, Y.; Takeoka, M.; Wada, N.; et al. Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 Tbit/s data channels. Commun. Phys.
**2019**, 2, 9. [Google Scholar] [CrossRef] - Kumar, R.; Qin, H.; Alléaume, R. Coexistence of continuous variable QKD with intense DWDM classical channels. New J. Phys.
**2015**, 17, 043027. [Google Scholar] [CrossRef] - LUXQUANTA. Available online: https://www.luxquanta.com/continuous-and-discrete-quantum-key-distribution-qkd-r-10-en (accessed on 3 November 2023).
- Ruihong, Q.; Ying, M. Research Progress of Quantum Repeaters. J. Phys. Conf. Ser.
**2019**, 1237, 052032. [Google Scholar] [CrossRef] - Louisa, S.; Momtchilb, P.; Elenic, D.; Romaind, A.; Norberte, L.; Thomasb, L. Security of trusted repeater quantum key distribution networks. J. Comput. Secur.
**2010**, 18, 61–87. [Google Scholar] [CrossRef] - Wang, S.; Yin, Z.-Q.; He, D.-Y.; Chen, W.; Wang, R.-Q.; Ye, P.; Zhou, Y.; Fan-Yuan, G.-J.; Wang, F.-X.; Chen, W.; et al. Twin-field quantum key distribution over 830-km fibre. Nat. Photonics
**2022**, 16, 154–161. [Google Scholar] [CrossRef] - Park, C.H.; Park, B.K.; Kim, Y.-S.; Baek, H.; Lee, S.-W.; Lim, H.-T.; Jeon, S.-W.; Jung, H.; Han, S.-W. 2 × N twin-field quantum key distribution network configuration based on polarization, wavelength, and time division multiplexing. npj Quantum Inf.
**2022**, 8, 48. [Google Scholar] [CrossRef] - Xie, Y.-M.; Lu, Y.-S.; Weng, C.-X.; Cao, X.-Y.; Jia, Z.-Y.; Bao, Y.; Wang, Y.; Fu, Y.; Yin, H.-L.; Chen, Z.-B. Breaking the Rate-Loss Bound of Quantum Key Distribution with Asynchronous Two-Photon Interference. PRX Quantum
**2022**, 3, 020315. [Google Scholar] [CrossRef] - Zhou, L.; Lin, J.; Xie, Y.-M.; Lu, Y.-S.; Jing, Y.; Yin, H.-L.; Yuan, Z. Experimental Quantum Communication Overcomes the Rate-Loss Limit without Global Phase Tracking. Online. Phys. Rev. Lett.
**2023**, 130, 250801. [Google Scholar] [CrossRef] [PubMed] - Quantum Repeaters. QuReP. 2010. Available online: http://www.quantumrepeaters.eu/ (accessed on 7 July 2023).
- Markus, W. Experimental Quantum Memory Applications and Demonstration of an Elementary Quantum Repeater Link with Entangled Light-Matter Interfaces; Ludwig-Maximilians-Universität München: München, Germany, 2012; Volume 102, Available online: https://www.bit.ly/3PtZqKM (accessed on 7 September 2023).
- New Quantum Repeaters Could Enable a Scalable Quantum Internet. Physics World. Available online: https://physicsworld.com/a/new-quantum-repeaters-could-enable-a-scalable-quantum-internet/ (accessed on 11 June 2023).
- Quantum Repeaters. Quantum Flagship. Available online: https://qt.eu/discover-quantum/underlying-principles/quantum-repeaters/ (accessed on 7 September 2023).
- Mlejnek, M.; Kaliteevskiy, N.; Nolan, D. Reducing spontaneous Raman scattering noise in high quantum bit rate QKD systems over optical fiber. arXiv
**2017**, arXiv:1712.05891. [Google Scholar] - Qi, B.; Zhu, W.; Qian, L.; Lo, H. Feasibility of quantum key distribution through a dense wavelength division multiplexing network. New J. Phys.
**2010**, 12, 103042. [Google Scholar] [CrossRef] - Schneider, T. Four-Wave-Mixing (FWM). In Nonlinear Optics in Telecommunications; Advanced Texts in Physics; Thomas, S., Ed.; Springer: Berlin/Heidelberg, Germany, 2004; pp. 167–200. ISBN 978-3-642-05772-4. [Google Scholar] [CrossRef]
- Eraerds, P.; Walenta, N.; Legré, M.; Gisin, N.; Zbinden, H. Quantum key distribution and 1-Gbps data encryption over a single fibre. New J. Phys.
**2010**, 12, 063027. [Google Scholar] [CrossRef] - Fenta, M.C.; Potter, D.K.; Szanyi, J. Fibre Optic Methods of Prospecting: A Comprehensive and Modern Branch of Geophysics. Surv. Geophys.
**2021**, 42, 551–584. [Google Scholar] [CrossRef] - Ciurana, A.; Martin, V.; Martinez-Mateo, J.; Poppe, A.; Soto, M.; Walenta, N.; Zbinden, H. Multiplexing QKD systems in Conventional Optical Networks. In 2012 QCRYPT; QCRYPT: Zürich, Switzerland, 2012; Available online: https://oa.upm.es/32937/1/qcrypt2012.pdf (accessed on 3 November 2023).
- Dimitris, Z.; Argiris, N.; Panagiotis, T.; Adam, R.; Christos, K.; Theofanis, S.; Fotini, S.; Eleni, T.; George, L.; Giannis, G.; et al. Coexistence Studies for DV-QKD Integration in Deployed RAN Infrastructure. In Proceedings of the 2022 International Workshop on Fiber Optics in Access Networks (FOAN), Valencia, Spain, 11–12 October 2022; IEEE: New York, NY, USA, 2022; pp. 6–9, ISBN 978-1-6654-6503-8. [Google Scholar] [CrossRef]

**Figure 1.**Sketch of a graph showing the approximate shape of the reflected noise of the classical channel in the band at approximately 1550 nm. In the middle is the central wavelength to which Rayleigh scattering corresponds. Then, at a distance of approximately 0.1 nm is the Brillouin scattering, and at a distance of 100 nm is the Raman scattering (both temperature dependent). In terms of noise, it is best to place the quantum channel in the anti-Stokes region 1 to 5 nm from the classical channel (red circle). Alternatively, a similar area might be used in the Stokes region.

**Figure 2.**The original route combining two opposite service channels (CH29 and CH30) with one quantum channel (CH32) is connected. The layout also includes optical power values at important locations in the route, which were obtained by measurement or calculation. The values CH29-r and CH30-r represent the possible remaining power that was passed through the DWDM filters toward the source or detector of the quantum signal.

**Figure 3.**Initial route from Phase I, modified for service channel attenuation testing. The main difference is the addition of a second SFP pair.

**Figure 4.**The figure shows what components of Raman noise produce errors in detecting a quantum signal. The total malicious Raman noise consists of the forward component CH30 and the backward component CH29.

**Figure 5.**Schematic of the final and functional route of the polygon. Compared to the previous design, it contains a number of different components. In particular, these are circulators and EDFAs whose signal is subsequently “trimmed” by using a CWDM filter.

**Figure 6.**Schematic diagram of one of the service channels with power values at various points along the optical route.

**Figure 7.**Graphs showing the spectra of both service channels (CH29 and CH30) in different parts of the optical route. The purple lines show the region of occurrence of the quantum channel (CH32).

**Figure 8.**The graphic describes the service channel optical power problem. The higher its power, the worse the effect it has on the quantum channel. In contrast, the more the service channel is attenuated, the lower the probability that it works properly. The “benevolence” in terms of power increases as the shared fiber shortens.

Manufacturer | ID Quantique (IDQ) |

QKD protocol | Coherent One-way (COW) |

Pulse generation rate | 1.25 GHz |

Key generation rate | 1.4 kbps |

Dynamic range | 10–14 dB |

Photon number | 0.03 |

Quantum channel | ⟶ 1551.72 nm CH32 –83.2 dBm ^{1} 1.4 kbps |

Service channel I | ⟶ 1553.33 nm CH30 –3.0 dBm ^{2} 2.7 Gbps |

Service channel II | ⟵ 1554.13 nm CH29 –3.0 dBm ^{2} 2.7 Gbps |

^{1}Based on own calculation.

^{2}Based on own power measurements.

**Table 2.**Quantum channel performance when combined with both service channels. The first column contains the attenuation added by the VOA to the already installed 20 dB.

SFP 29 and 30 | Key Rate (kbps) | QBER (%) | Visibility (%) |
---|---|---|---|

Turned off | 2.07 | 3.04 | 98.60 |

+20 dB | 2.04 | 3.22 | 98.40 |

+10 dB | 1.59 | 3.41 | 97.70 |

+7 dB | 1.26 | 4.10 | 97.20 |

+5 dB | 0.65 | 4.45 | 97.40 |

+4 dB | non-functional | 5.05 | 97.10 |

+3 dB | non-functional | 5.27 | 96.70 |

+2 dB | non-functional | 5.32 | 96.50 |

+1 dB | non-functional | 6.56 | 96.00 |

+0 dB | non-functional | 8.96 | 94.80 |

Connection | Key Rate (kbps) | QBER (%) | Visibility (%) |
---|---|---|---|

Direct | 2.11 | 3.33 | 98.70 |

20 km | 1.21 | 4.05 | 97.40 |

**Table 4.**Measurement results for five QKD configuration of the polygon. The table contains the Raman noise optical power values and basic system parameters.

Connection | Raman (dBm) | Key Rate (kbit/s) | QBER (%) | Visibility (%) |
---|---|---|---|---|

Direct | —— | 2.52 | 2.78 | 99.30 |

5 km | −112.75 | 2.19 | 3.57 | 98.00 |

10 km | −109.61 | 2.04 | 3.67 | 97.50 |

15 km | −107.63 | 1.69 | 3.92 | 97.50 |

20 km | −106.08 | 0.45 | 4.61 | 97.30 |

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**MDPI and ACS Style**

Klicnik, O.; Munster, P.; Horvath, T.
Multiplexing Quantum and Classical Channels of a Quantum Key Distribution (QKD) System by Using the Attenuation Method. *Photonics* **2023**, *10*, 1265.
https://doi.org/10.3390/photonics10111265

**AMA Style**

Klicnik O, Munster P, Horvath T.
Multiplexing Quantum and Classical Channels of a Quantum Key Distribution (QKD) System by Using the Attenuation Method. *Photonics*. 2023; 10(11):1265.
https://doi.org/10.3390/photonics10111265

**Chicago/Turabian Style**

Klicnik, Ondrej, Petr Munster, and Tomas Horvath.
2023. "Multiplexing Quantum and Classical Channels of a Quantum Key Distribution (QKD) System by Using the Attenuation Method" *Photonics* 10, no. 11: 1265.
https://doi.org/10.3390/photonics10111265