SCIENCE CHINA Information Sciences, Volume 63 , Issue 8 : 180504(2020) https://doi.org/10.1007/s11432-020-2886-x

## A universal simulating framework for quantum key distribution systems

• AcceptedApr 24, 2020
• PublishedJul 15, 2020
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### Abstract

Quantum key distribution (QKD) provides a physical-based way to conciliate keys between remote users securely. Simulation is an essential method for designing and optimizing QKD systems. We develop a universal simulation framework based on quantum operator descriptions of photon signals and optical devices. The optical devices can be freely combined and driven by the photon excitation events, which make it appropriate for arbitrary QKD systems in principle. Our framework focuses on realistic characters of optical devices and system structures. The imperfections of the devices and the non-local properties of a quantum system are taken into account when modeling. We simulate the single-photon and Hong-Ou-Mandel (HOM) interference optical units, which are fundamental of QKD systems. The results using this event-driven framework agree well with the theoretical results, which indicate its feasibility for QKD.

### Acknowledgment

This work was supported by National Key Research and Development Program of China (Grant No. 2018YFA0306400), National Natural Science Foundation of China (Grant Nos. 61627820, 61675189, 61622506, 61822115), Anhui Initiative in Quantum Information Technologies (Grant No. AHY030000). We also appreciate Dr. Xuebi AN and Yuyang DING of Anhui Qasky, Co. Ltd. for helpful discussion.

### Supplement

Appendix

We show the details regarding the model optical elements in Table tabdetiledcom. All input and output parameters are denoted by subscript $i$ and $o$, respectively.

beginlongtable

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• Figure 1

Model construction. (a) System layer: the tripartite optical devices of real-world QKD systems, which consist of the light source, manipulation, and detection units. The quantum states of photons are created by the light source, manipulated by the systems and the channels, and finally measured by detectors. (b) Modeling layer: devices and procedure modeling. Quantum optical devices are modeled as creator, measurer, and manipulator according to the three types of quantum operations in (a). Quantum states transfer the optical devices and are transformed. The quantum signals are passed through the devices through their input and output ports. (c) Implementation layer: realization of the models in modeling layer using C+ classes integrated with OMNet+. Specifically, each optical device is encapsulated as a component class, of which the input and output ports are driven by messages. The quantum pool is a custom-designed array to store the same kind of quantum states, and the quantum core is the processor of the quantum operations like Pauli operators and the projection measurements.

• Figure 2

Data structure for the depiction of PhotonPool. The quantum state, as a constitution of photons, is stored in a PhotonPool which is an array of photons. In PhotonPool, each photon consists of the superposition of photon states, which is the basic element of the data structure and contains the information of the degrees of freedom listed in Table 1.

• Figure 3

Hong-Ou-Mandel interference at a beam splitter. SPS: single-photon source; BS: beamsplitter; D: detector.

• Figure 4

(Color online) Schematic and simulation network of MZI. (a) Schematic diagram of MZI. SPS: single-photon source; BS: beamsplitter; PM: phase modulator; D: detector. (b) Network description of simulation program. src: single-photon source; bs: beamsplitter; phasemodulator: phase modulator; adapter: just for aesthetics; spd: detector; quantcore: QuantumCore. (c) Comparison of simulation results and theoretical calculations. The dotted red and yellow correspond to simulation results $P_{\rm~D1}$ and $P_{\rm~D2}$, respectively. The solid blue and green are theoretical curves derived from (24), respectively.

• Figure 5

(Color online) Schematic and simulation network of HOM interferometry. (a) Schematic diagram of HOM interferometry. SPS: single-photon source; BS: beamsplitter; D: detector. (b) Network description of simulation program. src: single-photon source; bs: beamsplitter; spd: detector; quantcore: QuantumCore. (c) Comparison of simulation results and theoretical calculations. The dotted red and solid blue correspond to simulation coincidence probability versus $\delta\theta$ and theoretical curves derived from (26), respectively. (d) The dotted red and solid blue correspond to simulation coincidence probability as a function of $\delta~t$ and theoretical curves derived from (27), respectively. The $\sigma$ is 65 GHz, which is a typical value for a 1550 nm laser.

• Table 1

Table 1Member variables definition of photon state

 Variable name Data type Explanation Delay Double The relative time delay between the photon states which in a same multi-photon states system RouteID Double The path where the photon state is propagating SpectralMu Double The mean of the Gaussian frequency distribution SpectralSigma Double The standard deviation of the Gaussian frequency distribution Phase Double The relative phrase between the photon states which in a same multi-photon states system Alpha Double The amplitude of the field in the horizontal direction Beta Double The amplitude of the field in the vertical direction DeltaPhase Double The difference between the phase angles of fields in horizontal and vertical directions Coefficient Double The normalization coefficient
• Table 2

Table 2Member variables definition of BS and PBS

 Component Variable name Data type Explanation Beamsplitter SplittingRatioR Double Reflectance SplittingRatioT Double Transmittance Loss Double Loss ExtinctionRatio Double ExtinctionRatio Loss Double Loss Polarization beamsplitter LossH Double The loss of the field in the horizontal direction LossV Double The loss of the field in the vertical direction
• Table 3

Table 3Common modeled optical elements

 Attenuator Bandpass filter Circulator Polarization modulator Phase modulator Isolator 1$\times$2 optical switch Waveplate Fiber Faraday mirror (FM)
• Table 4

Table 4Member variables definition of SPD

 Variable name Data type Explanation DetectionEfficiency Double The detection efficiency of the given wavelength ProbabilityDarkCount Double The dark count probability of the SPD ProbabilityAfterpulse Double The afterpulse probability of the SPD TimingJitter Double The jitter of click signal emission time ResolvesPhotonNumber Bool The flag of photon number resolution, when it is true, the SPD return photon number, otherwise it return click signal Enable Bool The flag of SPD on-off state, when it is true, the SPD responds the photon pulse, otherwise it does not work TimeWidth Double The duration of open gate for gate mode

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