Satellite-ground QKD downlink transmission layered model
阅读说明：本技术 一种星地qkd下行传输分层模型 (Satellite-ground QKD downlink transmission layered model ) 是由 刘涛 李佳佳 邱佳 王思佳 刘舒宇 于 2021-08-16 设计创作，主要内容包括：本发明适用于星地间量子密钥分发,提供了一种星地QKD下行传输分层模型。该方法考虑了大气折射效应的存在,在此模型下,考虑大气折射对链路距离带来的影响,对大气层的对流层和平流层进行分层,详细计算每一层的链路距离,最后得到整体经过大气折射后的链路距离。该发明充分考虑了当前星地量子密钥分发信号传输的实际情况,为实际的星地量子密钥分发系统设计提供一定的参考。(The invention is suitable for inter-satellite-ground quantum key distribution and provides a satellite-ground QKD downlink transmission layered model. The method considers the existence of atmospheric refraction effect, under the model, the influence of atmospheric refraction on the link distance is considered, the troposphere and the stratosphere of the atmosphere are layered, the link distance of each layer is calculated in detail, and finally the link distance after the atmospheric refraction is carried out on the whole is obtained. The invention fully considers the actual situation of current satellite-ground quantum key distribution signal transmission and provides a certain reference for the design of an actual satellite-ground quantum key distribution system.)
1. A satellite-to-ground QKD downlink transmission hierarchical model is characterized in that the total link distance of the satellite-to-ground QKD downlink transmission hierarchical model comprises:
according to the atmosphere layered structure, the troposphere is positioned at the lowest part of the atmosphere, the stratosphere is above the troposphere, and when the altitude exceeds 50km, the atmosphere refractive index is close to the vacuum refractive index 1, so that only the troposphere and the stratosphere are layered;
respectively solving the temperature pressure values of each layer by using the temperature pressure formulas of the troposphere and the stratosphere, and calculating the refractive index of each layer by using the obtained temperature pressure values;
and obtaining the linear path value of each layer by using the obtained refractive index of each layer, and finally adding the layers to obtain the final total link distance of signal transmission.
2. The satellite-ground QKD downlink transmission layering model according to claim 1, characterized in that the temperature and pressure values of each layer are obtained by using the temperature and pressure formulas of the troposphere and the stratosphere respectively, and the refractive index of each layer is calculated by using the obtained temperature and pressure values; the linear path value of each layer is obtained by utilizing the obtained refractive index of each layer, and finally, the layers are added to obtain the final total link distance of signal transmission, and the method comprises the following steps:
the temperature (T) and pressure (P) in the troposphere can be calculated using the following equations:
T＝T0-(h/1000)×6.5 (1)
P＝P0×(1-0.0065×h/288)5.255 (2)
the temperature and air pressure calculation formula in the stratosphere is as follows:
the temperature and pressure values of the layers were obtained by dividing the atmosphere of 50km or less into 10 layers according to the equations (1) to (4).
The relationship between the refractive index of air and the pressure and temperature of air over a range of optical wavelengths can be expressed as:
we can obtain the refractive indices of the different layers from equation (5).
To obtain the link distance after layered refraction, we refer to the relevant refraction angle in fig. 2 to calculate, and we denote the upper latitude bound of the ith layer as HiThen the linear path within the layer is determined as
The rest of the light path is positioned in vacuum,
where the index N corresponds to the last atmosphere, N10.
Then the total link distance between the satellite and the ground station after layered refraction is
Technical Field
The invention relates to the field of communication, in particular to a satellite-ground QKD downlink transmission layered model.
Background
Quantum Key Distribution (QKD) has started in the last 80 th century, and its security has been ensured by quantum unclonable principles and uncertainty principles. The optical fiber quantum communication is limited by terrain, and is limited by that the single transmission distance can only be about hundred kilometers, etc., so that the global quantum communication network is not enough to be constructed only by the optical fiber quantum communication at present. The satellite quantum communication technology utilizes a satellite and the ground to establish a communication network, and can realize quantum communication in a global range.
The establishment of satellite-mediated quantum links is a difficult task, and the low earth orbit has the advantages of low optical loss, low cost, easy operation and the like, so that the low earth orbit becomes the first choice of many existing satellite earth quantum communication schemes at present, and the performance of a downlink is better than that of an uplink.
Disclosure of Invention
The inventor finds that most of the satellite-ground quantum communication link models do not consider the existence of atmospheric refraction effect when performing performance analysis, neglects the elongation of link distance caused by atmospheric refraction in the actual transmission process, and the condition influences the performance analysis to a certain extent. In order to solve the problem, the invention provides a layered model of satellite-ground link transmission, which considers the existence of atmospheric refraction effect, under the model, considers the extension of link distance caused by atmospheric refraction in the actual transmission process, layers the troposphere and the stratosphere of the atmosphere, calculates the link distance of each layer in detail, and finally obtains the link distance after the atmospheric refraction of the whole body, so that the performance analysis performed by using the link distance is closer to the actual scene, and a certain reference is provided for the design of the actual satellite-ground quantum key distribution system.
The specific method steps of the invention are as follows:
a satellite-to-ground QKD downlink transmission layered model, the satellite-to-ground QKD downlink transmission layered model total link distance comprising:
according to the atmosphere layered structure, the troposphere is positioned at the lowest part of the atmosphere, the stratosphere is above the troposphere, and when the altitude exceeds 50km, the atmosphere refractive index is close to the vacuum refractive index 1, so that only the troposphere and the stratosphere are layered;
respectively solving the temperature pressure values of each layer by using the temperature pressure formulas of the troposphere and the stratosphere, and calculating the refractive index of each layer by using the obtained temperature pressure values;
and obtaining the linear path value of each layer by using the obtained refractive index of each layer, and finally adding the layers to obtain the final total link distance of signal transmission.
The technical scheme provided by the invention has the beneficial effects that:
the existence of atmospheric refraction effect is considered in the satellite-ground quantum key distribution process, the extension of atmospheric refraction link distance after effective layering is taken into the consideration range, the actual situation during transmission is considered, and finally the performance simulation result obtained according to the method is more accurate.
Drawings
FIG. 1 shows a satellite-to-ground QKD downlink transmission layering model;
FIG. 2 shows an enlarged ray path corresponding to FIG. 1 used to calculate link distance;
figure 3 shows a bit error rate comparison graph of the presence or absence of atmospheric refraction effects at different wavelengths (Case1: consider the presence of atmospheric refraction effects; Case2: do not consider the presence of atmospheric refraction effects).
Detailed Description
The invention is described in further detail below with reference to the drawings and examples of the specification. It should be understood that the specific examples described herein are intended to be illustrative only and are not intended to be limiting.
The specific method steps of the invention are as follows:
(1) and establishing a satellite-ground QKD downlink transmission hierarchical model.
Since the temperature and pressure in the actual atmosphere vary with altitude, so that the refractive index also varies, the actual path of the signal light from the satellite to the ground receiving end should be curved, such as OQ in fig. 11Q2…QNS is shown by the curve with arrows. In this case, the signal from the satellite arrives at zenith angle ξaBelow, rather than below the true zenith angle ξ. We use the satellite-ground QKD downlink transmission hierarchical model shown in FIG. 1 to study the satellite-ground quantum communication characteristics.
When considering the variation of refraction versus altitude, we divide the atmosphere into N layers and assume that the refractive index of each layer is uniform in order to calculate the link distance. In this case, the preceding transmission path OS becomes a meandering path OQ1Q2...QN。
(2) Effective atmosphere stratification
According to the atmosphere layered structure, the troposphere is located at the lowest part of the atmosphere, the thickness of the troposphere is about 8-18 km, and the temperature of the troposphere is reduced along with the increase of the altitude. Above the troposphere is the stratosphere, which rises in temperature with increasing altitude. When the altitude exceeds 50km, the refractive index of the atmosphere approaches that of vacuum 1, so we only delaminate the stratosphere as well as the stratosphere.
(3) Calculating the linear path of each layer after atmospheric refraction
The temperature and pressure of each layer after layering are respectively obtained by different temperature and pressure formulas of the troposphere and the stratosphere, then the temperature and pressure are substituted into an air refractive index formula to obtain the refractive index of each layer, and the linear path of each layer is obtained by using the correlation angle shown in the graph 1 and the graph 2 by using the different refractive index of each layer.
(4) Calculating the total link distance after atmospheric refraction
And adding the linear paths of each layer to obtain the total link distance.
(5) Simulation analysis
And substituting the obtained total link distance considering the atmospheric refraction effect into a formula related to the link distance to perform performance simulation analysis.
The technical scheme provided by the invention has the beneficial effects that:
the existence of atmospheric refraction effect is considered in the satellite-ground quantum key distribution process, the extension of atmospheric refraction link distance after effective layering is taken into the consideration range, the actual situation during transmission is considered, and finally the performance simulation result obtained according to the method is more accurate.
In the embodiment, signal transmission is carried out at a satellite transmitting end and a ground receiving end based on satellite-ground quantum key distribution. Under the model and the method designed by the invention, the final bit error rate simulation analysis is closer to the actual situation, and the following specific steps are carried out:
(1) and (3) establishing a satellite-ground QKD downlink transmission hierarchical model, wherein the established model is shown in figure 1.
To calculate the link distance, we divide the atmosphere into N layers and assume that the refractive index of each layer is uniform, taking into account the variation of refraction with altitude. In this case, the preceding transmission path OS becomes a meandering path OQ1Q2...QN。
(2) And effectively layering the atmosphere.
According to the atmosphere layered structure, the troposphere is located at the lowest part of the atmosphere, the thickness of the troposphere is about 8-18 km, and the temperature of the troposphere is reduced along with the increase of the altitude. Above the troposphere is the stratosphere, which rises in temperature with increasing altitude. When the altitude exceeds 50km, the atmospheric refractive index approaches the vacuum refractive index 1, so we only delaminate the stratosphere and the stratosphere, and totally separate 10 layers below 50km (N is 10).
(3) Calculating the linear path of each layer after atmospheric refraction, and then adding to obtain the final total transmission distance.
The temperature (T) and pressure (P) in the troposphere can be calculated using the following equations:
T＝T0-(h/1000)×6.5 (1)
P＝P0×(1-0.0065×h/288)5.255 (2)
the temperature and air pressure calculation formula in the stratosphere is as follows:
the temperature and pressure values of the layers were obtained by dividing the atmosphere of 50km or less into 10 layers according to the equations (1) to (4).
The relationship between the refractive index of air and the pressure and temperature of air over a range of optical wavelengths can be expressed as:
we can obtain the refractive indices of the different layers from equation (5).
To obtain the link distance after layered refraction, we refer to the relevant refraction angle in fig. 2 to calculate, and we denote the upper latitude bound of the ith layer as HiThen the linear path within the layer is determined as
The rest of the light path is positioned in vacuum,
where the index N corresponds to the last atmosphere, N10.
Then the total link distance between the satellite and the ground station after layered refraction is
(4) Simulation analysis
When the decoy BB84 protocol is adopted to enter the planetary ground QKD, the corresponding error rate calculation formula is as follows:
the total signal transmission efficiency Ω is:
Ω＝ΩgeoΩhtmTchaγc (10)
the total link distance after atmospheric layered refraction is substituted into the L of the formula (11) to obtain the error rate after atmospheric layered refraction is finally considered, and the obtained error rate analysis and comparison result considering the atmospheric refraction effect and not considering the atmospheric refraction effect is shown in fig. 3, so that the necessity of considering the atmospheric refraction effect is fully verified.
The process of the present invention is discussed in detail below.
Introduction to the invention
Quantum Key Distribution (QKD) has started in the last 80 th century, and its security has been ensured by quantum unclonable principles and uncertainty principles. The optical fiber quantum communication is limited by terrain, and is limited by that the single transmission distance can only be about hundred kilometers, etc., so that the global quantum communication network is not enough to be constructed only by the optical fiber quantum communication at present. The satellite quantum communication technology utilizes a satellite and the ground to establish a communication network, and can realize quantum communication in a global range.
The low earth orbit has the advantages of low optical loss, low cost, easy operation and the like, so the low earth orbit becomes the first choice of a plurality of satellite-earth quantum communication schemes at present. The prior literature provides reference for others to research satellite-to-ground quantum communication, but the prior literature does not consider the influence of atmospheric refraction on the performance of a link under actual conditions in the research process. The existing documents consider atmospheric refraction, and carry out layering calculation on the atmosphere to calculate the length of the geometric distance between the satellite and the ground station after the atmospheric refraction, but on one hand, the existing documents do not carry out comparative analysis on the error rates without layering refraction and layering refraction, and do not effectively prove the necessity of adopting layering refraction analysis; on the other hand, the troposphere, which has a large influence on the atmospheric turbulence, is not stratified when the atmosphere is stratified. More importantly, the intensity of the atmospheric turbulence is different at different heights, and the atmospheric turbulence is regarded as a uniform value though the atmospheric layer is layered in the existing literature.
In addition, the existing documents do not consider the influence brought by different wavelength signals, only use a single wavelength, and actually, the influence of background light, turbulence and other factors on different signal light wavelengths is different, so that different wavelength conditions need to be analyzed; based on the analysis, the influence of different signal light wavelength signals on the bit error rate of inter-satellite quantum key distribution under the two conditions of considering layered refraction and not considering layered refraction is mainly researched, a satellite-ground link transmission model is firstly established, under the model, the influence of atmospheric refraction on link distance is considered, a troposphere and a stratosphere of an atmosphere are layered, a QKD quantum bit error rate calculation formula considering different atmospheric turbulence intensities corresponding to different heights is given, then the change of the bit error rate under different wavelengths, different zenith angles and different background light conditions is calculated and analyzed by using the given formula, and the research result can provide a certain reference for the actual design of a satellite-ground quantum key distribution system.
Two, transmission model
1. Two zenith angles of satellite-ground link
In a satellite link, the zenith angle is the angle between the vertical direction of the viewer and the pointing direction of the satellite, and changes as the satellite moves. Downlink refers to the transmission of signals from a satellite to a ground station. As shown in fig. 1, when the variation of the atmospheric refractive index with altitude is not considered, the zenith angle is an angle ξ between a line OS between the ground reception station (O) and the satellite (S) and a line CO between the geocenter (C) and the ground reception station (O), which is called the true zenith angle. However, since the temperature and pressure in the actual atmosphere vary with altitude, the refractive index (the air responsive index) also varies, and the actual path of the signal light from the satellite to the ground receiving end should be curved, such as OQ in fig. 11Q2…QNS is shown by the curve with arrows. In this case, the signal from the satellite arrives at zenith angle ξa(the apparent zenith angle) rather than the true zenith angle. In the actual process of satellite-ground quantum communication, the quantum communication characteristics should be analyzed by using the apparent zenith angle, and most of the existing researches adoptThe true zenith angle does not consider the influence of atmospheric refraction on the satellite-ground link. Therefore, the zenith angle signal transmission model shown in fig. 1 is used herein to study the satellite-ground quantum communication characteristics.
Apparent zenith angle xiaThe relation formula between the real zenith angle xi is as follows:
wherein n is01.00027 is the refractive index of the sub-atmospheric layer.
In satellite-to-ground quantum communication, we assume that the orbit is circular, the earth radius R is 6371km, and H is the height of the satellite from the ground. When not considering the variation of the refractive index with altitude, the link distance OS between the ground station and the satellite can be calculated using the triangular OCS shown in fig. 1:
when considering the variation of refraction versus altitude, to calculate the Link distance (Link distance), the atmosphere may be divided into N layers, and the refractive index of each layer is assumed to be uniform. In this case, the preceding transmission path OS becomes a meandering path OQ1Q2...QN. According to the atmosphere layered structure, the troposphere (troposphere) is located at the lowest part of the atmosphere, the thickness of the troposphere is about 8-18 km, and the temperature of the troposphere decreases along with the increase of the altitude. Above the troposphere is the Stratosphere (Stratosphere), which rises in temperature with increasing altitude. When the altitude exceeds 50km, the refractive index of the atmosphere approaches that of vacuum 1, so we only delaminate the stratosphere as well as the stratosphere.
As mentioned above, while the near-surface atmospheric turbulence has a large influence on the link characteristics, the existing documents only consider the stratification of the stratosphere and do not subdivide the stratosphere. The method is improved on the basis that convection layers are also subdivided, and the convection layers are divided into 10 layers in total under 50 km. Since the change laws of the air pressure and the temperature in the troposphere and the stratosphere are different with the change of the altitude, it is necessary to perform the stratification process on the troposphere as well. In addition, although the atmosphere is layered, the turbulence is not layered.
The relationship between the refractive index of air and the pressure and temperature of air over a range of optical wavelengths can be expressed as:
where λ is the optical wavelength in μm, P is the gas pressure in mb, and T is the common temperature in Kelvin.
The temperature and pressure in the troposphere can be calculated using the following equations:
T＝T0-(h/1000)×6.5 (15)
P＝P0×(1-0.0065×h/288)5.255 (16)
wherein, T0Sea level temperature of 288K, h is height from ground in m, P0Is the gas pressure at h-0 and is 101.325KPa。
The temperature and air pressure calculation formula in the stratosphere is as follows:
wherein (the temperature change rate) Δ1＝-6.5K/km，Δ2＝1.0K/km，Δ3＝3.0K/km。ha＝11km，hb＝22km，hc＝32km，hd50 km; m is the molecular weight of the dry air of 28.10, g is the acceleration of gravity of 9.8M/s2D is the universal attraction constant 8.314 J.mol-1·k-1。
The temperature and pressure values of the layers were obtained from the equations (3) to (6) after dividing the atmosphere layer of 50km or less into 10 layers, as shown in table 1.
Table 1 Temperature and pressure values of each layer
Layering
Height (Km)
Temperature (K)
Pressure (mb)
1
2
275
794.88
2
4
262
616.29
3
6
249
471.67
4
8
236
355.85
5
10
223
264.21
6
11
217
226
7
20
217
54.7
8
32
229
8.68
9
47
271
1.11
10
50
271
0.67
To obtain the link distance after layered refraction, we refer to the relevant refraction angle in fig. 2 for calculation, fig. 2 enlarges the ray path of fig. 1 and shows the relevant refraction angle, and the upper latitude boundary of the ith layer is represented as HiThen the linear path within the layer is determined as
Wherein Γ (ξ)a)＝σi(ni)-σ0i(ξa)+θi。
The rest of the light path is positioned in vacuum,
where N corresponds to the last hierarchical level, Λ ([ xi ])a)＝υN-δN+ωN(ξa)-ω(ξa)。
Then the total link distance between the satellite and the ground station after layered refraction is
The link distance after the refraction of the non-lamination and the refraction of the lamination can be calculated by using the formula (13) and the formula (21), and it can be seen that the link distance gradually increases with the increase of the zenith angle, no matter the lamination or the non-lamination, and the difference value between the link distance and the zenith angle is larger and larger. Therefore, if the link distance of non-layered refraction is adopted when the performance of the satellite-ground quantum communication system is analyzed, the result is influenced to a certain extent, and especially under the condition of large zenith angle, the influence cannot be ignored.
2. Background light noise and detector dark count
In a satellite-ground channel environment, the optical signal detector has a response area with larger wavelength, and background light in the wavelength range can be received by the receiver, so that the error rate is increased. In addition, the presence of detector dark counts also affects the bit error rate.
We consider the background radiation source model, i.e. the background as being generated by a uniform radiation source, the background rate can be expressed as:
B＝Pb/E (22)
in the formula: pbRepresenting background light noise power and E representing photon energy. Background light noise power PbCan be expressed as:
Pb＝HbΩfovπr2Δλ (23)
wherein HbIs the intensity of the background light radiation in Wm-2sr-1μm-1，Arec，ΩfovAnd Δ λ are the telescope aperture, field of view, and filter bandwidth, respectively, and r is the radial extent of the primary optics.
Substituting formula (23) into formula (22) and obtaining the final background rate of h/λ from E ═ hc/λ
Let NbFor the single photon counting rate caused by background light, the method has the steps that the time window delta t of the satellite-ground quantum key distribution
In addition to background light, the dark count of the detector can also cause additional noise. Since the satellite-ground quantum communication generally utilizes the polarization state to carry information, the receiving end usually employs four same detectors to detect, and the dark count rate of each detector is assumed to be fdarkThen, count dark NdWithin the time window Δ t:
Nd＝4fdarkΔt (26)
3. atmospheric turbulence and atmospheric transmission rate
The atmospheric turbulence is one of the main factors causing signal attenuation, and the turbulence intensity is the refractive index structure constantTo indicate. The Kolmogorov model is adopted to research the influence of atmospheric turbulence on the satellite-ground quantum communication performance, wherein the refractive index structural constant(unit is m)-2/3) Comprises the following steps:
whereinFor the temperature structure parameter, λ is the wavelength of the signal light in microns, P is the gas pressure in mb, and T is the temperature in K.
Calculating the refractive index structure constant at different signal wavelengths by using the formula (27)As can be seen from equation (27), the refractive index structure constant is closely related to the air pressure and temperature, and the air pressure and temperature are different at different altitudes, so that when the atmosphere is layered, the atmospheric turbulence is also required to be layered. Further, the longer the wavelength of the signal light, the smaller the refractive index structure constant, indicating that the long-wavelength signal is less affected by turbulence. It follows that quantum communication with long wavelength signals into the planet is recommended when only the effects of atmospheric turbulence are considered.
For a satellite-to-ground quantum key distribution system, the atmospheric transmittance (atmospheric transmittance) also varies with the zenith angle, TatmCan be expressed as:
where τ (0) is the atmospheric transmission at zenith angle of 0 and ξ is the zenith angle. According to the atmospheric transmission spectrum, the wavelength is 810nmAt wavelength of 1550nmWavelength of 3800nm
The change of the atmospheric transmittance along with the zenith angle under different wavelength conditions can be calculated by using the formula (28), the longer the wavelength is, the higher the atmospheric transmittance is, and the atmospheric transmittance gradually decreases along with the increase of the zenith angle under the same zenith angle, so that the influence of the large zenith angle on the channel transmission rate is relatively bad.
4. Error rate of satellite-to-ground QKD
When the decoy BB84 protocol is adopted to enter the planetary ground QKD, the corresponding error rate calculation formula is as follows:
wherein e0Is the probability of errors being caused by noise,edetthe probability of incorrect bit values due to polarization crosstalk is determined by the system stability; μ is the signal average photon number; y is0Is the background detection probability, including contributions of sky radiation and detector dark counts, the calculation formula is as follows:
Y0＝NbΩhtm+Nd (30)
wherein N isbΩhtmIs the probability of detecting sky noise photons, ΩhtmIs defined as
Ωhtm＝ΩrecΩspeΩdet (31)
Ωspe，Ωdet，ΩrecRespectively the efficiency of transmission through the spectral filter, the efficiency of photon detection and the efficiency of optical transmission through the remaining reception.
The total signal transmission efficiency Ω in this scheme is:
Ω＝ΩgeoΩtransΩhtm (32)
wherein omegageoIs a transmitter andthe angular dependent efficiency of the coupling between the receiver apertures can be given by the Friis equationApproximate calculation, the equation assumes a uniformly illuminated transmitter aperture, L denotes link distance, DTAnd DRThe apertures of the transmitter and receiver, respectively. OmegatransIs the transmission efficiency related to the angle related to atmospheric scattering and absorption, neglecting the effect of atmospheric turbulence. The prior literature introduces a turbulent atmospheric transmission factor gamma (one in the interval 0, 1) in a bit error rate model]And larger gamma indicates weaker turbulence) is a structural constant associated with the refractive indexRelated functions and having a certain inverse relation:
when the atmosphere is layered, the turbulent atmosphere transmission factor gamma is correspondingly improved, and the improved turbulent atmosphere transmission factor is expressed as gammac：
At this time, the total signal transmission efficiency Ω becomes:
Ω＝ΩgeoΩhtmTatmγc (35)
taking into account different layered refractive index structure constantsObtained gammacWith the variation of the wavelength, it can be seen that the turbulent atmospheric transmission factor increases with the increase of the wavelength, because the long wavelength reduces the effect of the turbulence to some extent, so that the efficiency of the atmospheric transmission under the effect of the turbulence becomes higherGood results are obtained.
Third, simulation analysis
In order to analyze the effect of different signal light wavelengths on the performance of the satellite-to-ground QKD, signal light wavelengths of 810nm, 1550nm and 3800nm, all in the atmospheric window, were used in the research process herein. And (3) simulating and analyzing the change of the error rate under the zenith angle without layered refraction and layered refraction along with the zenith angle, and considering the contribution to the error rate under different wavelength conditions. The simulation parameters are shown in table 2 below.
Table 2 The simulation parameters
The error rate under the conditions of non-layered refraction of different wavelengths and layered refraction varies with the zenith angle. FIG. 3 shows the error rate with zenith angle of three different signal light wavelengths of 810nm, 1550nm and 3800nm based on the same background light (clear day) without considering layered refraction and with considering layered refraction. The following conclusions can be drawn from the figure: 1) under the same wavelength, the error rate gradually rises along with the increase of the zenith angle, and the error rate after layered refraction is always larger than that when the layered refraction is not carried out. 2) And (3) respectively considering the conditions of non-layered refraction and layered refraction, wherein when the zenith angle is fixed, the longer the wavelength is, the higher the error rate is, and the longer the wavelength is, the more obvious the change trend of the error rate along with the zenith angle is.
Fourth, conclusion
The influence of error rates of three different signal light wavelengths of 810nm, 1550nm and 3800nm in satellite-ground quantum key distribution under the conditions of considering layered refraction and not considering layered refraction is researched, and the error rate variation along with zenith angles under different wavelength conditions is simulated by utilizing a satellite-ground decoy state BB84 protocol error rate model. The result shows that the quantum error rate has slight change under a small zenith angle, the increase of the zenith angle has great influence on the performance of a quantum channel, so that the quantum error rate is continuously increased, and in addition, in order to obtain better communication performance, experiments need to be carried out under the condition of clear weather at night. In addition, in the conventional research, the long wavelength can reduce the influence of the atmospheric turbulence and the background light noise, but in our research, we find that even if the long wavelength weakens the influence of the atmospheric turbulence and the background light noise, the error rate is not reduced in the case of the long wavelength compared with the short wavelength because the aperture coupling efficiency has a larger influence on the overall signal transmission efficiency than the turbulence, and further influences the error rate, so that the aperture coupling efficiency needs to be improved to obtain a lower error rate. In the research, parallax caused by earth rotation is ignored, and the research result can provide certain reference for the actual satellite-ground quantum key distribution communication design.
In the description, each part is described in a progressive manner, each part is emphasized to be different from other parts, and the same and similar parts among the parts are referred to each other.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.