CN1224210C - Quantum Encoders and Decoders for Phase-Modulated Polarization State and Their Applications - Google Patents

Abstract

The invention relates to a special device for quantum secret communication in the communication field and an application method thereof, in particular to a quantum encoder and a decoder for phase modulation polarization state and a polarization compensation method for the quantum secret communication; the four-state quantum encoder and decoder consists of a phase-polarization controller and a true random generator; six state quantumThe encoder and the decoder are composed of two phase-polarization controllers and a synchronous trigger; the method has the advantages that the polarization distortion caused in the signal transmission process is effectively compensated through the quantum encoder and the decoder for modulating the polarization state by the phase in the quantum cryptography communication, and the error rate is greatly reduced to 10^-5The modulation speed is from several tens of hertz to several gigahertz.

Description

Quantum Encoders and Decoders for Phase-Modulated Polarization State and Their Applications

Technical field

The invention relates to special equipment for quantum secure communication in the communication field and an application method thereof, in particular to a quantum encoder and decoder for phase modulation polarization state and a polarization compensation method for quantum secure communication.

Background technique

In the existing quantum cryptography communication technology, there are three types of protocols such as BB84 protocol, B92 protocol and E91 protocol, and three coding methods such as two-state coding, four-state coding and six-state coding. The BB84 protocol belongs to the four-state coding method, while the B92 protocol and the E91 protocol belong to the two-state coding method. The efficiency of the four-state coding method is relatively high, while the efficiency of the two-state coding method is halved.

The BB84 protocol usually adopts the phase modulation encoding method, that is, two identical Mach-Zehnder interferometers are used as the encoder and decoder. The bit error rate of this encoding method is mainly determined by the interference contrast ratio of the Mach-Zehnder interferometer in addition to the electrical noise. decision, and the interference contrast is determined by the coherence of light, because the coherence of light is inevitably destroyed in the process of modulation and transmission, and once the coherence is destroyed, it cannot be compensated, therefore, the bit error rate of this coding method relatively high.

Although the BB84 protocol can also be implemented by using four non-orthogonal linear polarization states or a four-state encoding method of two linear polarizations plus two circular polarization states, there is no technical breakthrough yet.

The B92 protocol usually has two methods of phase modulation and polarization modulation. The phase modulation coding method is basically the same as the BB84 protocol, except that the B92 protocol uses binary coding, and the efficiency is halved; while the polarization modulation coding method usually uses two linear polarization states of photons. Coding, that is, using electro-optic crystals (such as KD ^* P, LiNbO ₃ , etc.) or Pockels cells to modulate and code the two linear polarization states of photons, because the half-wave voltage of electro-optic crystals or Pockels cells is very high (several thousand volts), use It is very inconvenient, and it is difficult to achieve high-speed encoding, especially the polarization state of light is easily affected by factors such as stress birefringence and polarization mode dispersion in the optical fiber during transmission, as well as environmental interference, so the bit error rate is also relatively high .

The E91 protocol uses entangled photons for encoding. Because it is difficult to generate entangled photons and the required equipment is expensive, it is difficult to popularize and apply.

Contents of Invention

The purpose of the present invention is to provide a phase modulation polarization state quantum encoder and decoder, using the method of phase modulation polarization state to manufacture the phase modulation polarization state quantum encoder and decoder, and use the encoder to randomly prepare six photons of different polarization states, that is, photons of six non-orthogonal polarization states such as linear polarization of 0°, 45°, 90°, and 135°, and left-handed and right-handed circular polarization. The decoder can also be used to randomly generate six kinds of The non-orthogonal polarization state measurement base detects and decodes photons of six non-orthogonal polarization states; the encoder and decoder can be used for the quantum cryptography of two-state, four-state and six-state encoding of the BB84 protocol and the B92 protocol communication.

The purpose of the present invention is also to provide a method for the polarization compensation of the phase-modulated polarization state quantum encoder and decoder in the quantum secure communication, and adopt the phase-modulated polarization state technology to effectively control the polarization state distortion caused in the signal transmission process. The compensation can greatly reduce the bit error rate, the bit error rate can be reduced to 10 ^-5 , and the modulation speed ranges from tens of Hz to several GHz, which can be used for quantum cryptography communication of BB84 protocol and B92 protocol.

The phase modulation polarization state quantum encoder and decoder of the present invention include a four-state quantum encoder and decoder and a six-state quantum encoder and decoder.

Described four-state quantum encoder is made up of a phase-polarization controller and a true random generator, and optical path is as shown in Figure 2, when phase--the input voltage of the phase modulator 4 in the polarization controller is respectively: 0, During four voltages of V ₀ /2, V ₀ , and 3V ₀ /2 volts (V ₀ is a half-wave voltage), the phase modulator 4 generates phase changes of 0, π/2, π, and 3π/2 respectively. Therefore, The polarization states of phase-polarization controller output light are: 45° linear polarization, right-handed circular polarization, 135° linear polarization, left-handed circular polarization and other four non-orthogonal polarization states. The input voltage of the phase modulator 4 is provided by a true random generator 7, which can randomly generate four output voltages: 0, V ₀ /2, V ₀ , 3V ₀ /2 volts. In this way, we have developed a four-state quantum encoder composed of a phase-polarization controller and a true random generator. The four-state quantum encoder randomly prepares photons of four non-orthogonal polarization states, namely 45° linear polarization, Photons with four non-orthogonal polarization states: right-handed circular polarization, 135° linear polarization, and left-handed circular polarization.

The phase-polarization controller is composed of a polarization beam splitter, a phase modulator and a polarization-maintaining optical fiber. The optical path is shown in Figure 1. A beam of linearly polarized light is incident on the polarization beam splitter 1, and is divided into two beams whose polarization directions are perpendicular to each other. Linearly polarized light I and II, beam I enters polarization beam splitter 6 through polarization maintaining fiber 2, phase modulator 4 and polarization maintaining fiber 5, beam II enters polarization beam splitter 6 through polarization maintaining fiber 3, when beam I and When the optical path of beam II satisfies: n ₁ L ₃ =n ₁ L ₂ +n ₁ L ₅ +n ₂ L ₄ , (n ₁ , n ₂ are the refractive indices of the polarization-maintaining fiber and the phase modulator respectively, L ₂ , L ₃ and L ₅ are the lengths of the polarization maintaining fibers 2, 3, and 5 respectively, and L ₄ is the length of the phase modulator 4), and the polarization interference between the light beam I and the light beam II occurs at the polarization beam splitter 6, and the polarization of the output light The state is determined by the phase difference of these two beams of light, and the size of the phase difference is controlled by the phase modulator 4. When the input voltage of the phase modulator 4 is from: 0--2V ₀ volts (V ₀ is the half wave of the phase modulator When the voltage (about 10 volts) changes continuously, the phase modulator 4 can produce a phase change from: 0--2π, therefore, the polarization state of the corresponding output light can be from: 45° linear polarization--right-handed elliptical polarization-- Right-handed circular polarization--135° linear polarization--left-handed circular polarization--left-handed circular polarization changes continuously.

The four-state quantum decoder consists of a phase-polarization controller and a true random generator, which are used to randomly generate four groups of non-orthogonal polarization state measurement bases, and use these four groups of measurement bases to pair four non-orthogonal The photons in the polarization state are detected and decoded. The four groups of non-orthogonal polarization state measurement bases are: 45° linear polarization, right-handed circular polarization, 135° linear polarization, and left-handed circular polarization, which correspond to the input of the phase modulator 4 Voltage: 0, V ₀ /2, V ₀ , 3V ₀ /2 volts. That is to say, when the true random generator 7 randomly generates four output voltages: 0, V ₀ /2, V ₀ , 3V ₀ /2 volts, the four-state quantum decoder can randomly generate four sets of non-orthogonal polarization states Measurement base.

The method of using the four-state quantum encoder and decoder to carry out the quantum cryptography communication of the BB84 protocol is to realize the BB84 protocol quantum cryptography communication of "two linear polarization states plus two circular polarization states" 4-state encoding. The optical path is shown in Figure 3, and the method is as follows: the sender (Alice) uses a four-state quantum encoder to randomly prepare photons in four non-orthogonal polarization states, and transmits them to the receiver (Bob) through an optical fiber. The decoder randomly generates four groups of non-orthogonal polarization state measurement bases, and detects the four non-orthogonal polarization state photons sent by the sender. When a photon is detected, the receiver sends the measurement bases used through the public channel To the sender, the sender tells the receiver that the measurement base is selected correctly, and then the sender and the receiver retain the corresponding bits when the base is consistent, and discard other data, and the receiver publishes some bits at will for the sender to confirm whether there is an error. Finally, after the sender confirms that it is correct and no one is eavesdropping, the remaining bit sequence is reserved as a codebook.

Described six-state quantum encoder is made up of two phases--polarization controllers and a synchronous trigger, and the optical path is as shown in Figure 4, and the method is as follows: these two phases--polarization controllers are rotated at an angle of 45° to make them The polarization direction of the polarizing beam splitter is 45°, so that the 45° and 135° linearly polarized light output by the first phase-polarization controller becomes the second phase-polarization controller. 0° and 90° linearly polarized light, while the left-handed and right-handed circularly polarized light output by the first phase-polarization controller is still left-handed and right-handed circularly polarized for the second phase-polarization controller Light, therefore, for the second phase--the polarization controller, there are input photons of four polarization states, that is, 0°, 90° linear polarization and left-handed, right-handed circular polarization, when the second phase-- When the input voltages of the phase modulator of the polarization controller are: 0, V ₀ /2, V ₀ , 3V ₀ /2 volts, the polarization states of the output photons may be: 0°, 45°, 90°, 135 ° linear polarization and one of six non-orthogonal polarization states such as left-handed and right-handed circular polarization. The relationship between the polarization state of the output photon and the input voltage of the two phase modulators is shown in Table 1.

Table 1 The relationship between the polarization state of the output photon and the input voltage of the two phase modulators

It can be seen from Table 1 that the polarization state of the output photons is controlled by the input voltages of the two phase modulators in the two phase-polarization controllers. When the input voltages of the two phase modulators are randomly selected as 0, V ₀ /2, When V ₀ , 3V ₀ /2 volts, photons of six non-orthogonal polarization states such as 0°, 45°, 90°, 135° linear polarization and left-handed and right-handed circular polarization can be randomly generated. In this way, we have developed a six-state quantum encoder composed of two phase-polarization controllers and a synchronous trigger.

The structure of the six-state quantum decoder is exactly the same as that of the six-state quantum encoder, and its function is to randomly generate six groups of non-orthogonal polarization state measurement bases to detect and decode six non-orthogonal polarization state photons, which The six groups of non-orthogonal polarization state measurement bases are: 0°, 45°, 90°, 135° linear polarization measurement bases and left-handed and right-handed circular polarization measurement bases. It can be seen from Table 1 that when the true random generator 7 randomly generates four output voltages: 0, V ₀ /2, V ₀ , 3V ₀ /2 volts, the six-state quantum decoder can randomly generate six sets of non-orthogonal polarizations state measurement basis.

The method of using a six-state quantum encoder and decoder to perform quantum cryptography communication of the BB84 protocol is as follows: the optical path is shown in Figure 5, and the sender uses a six-state quantum encoder to randomly prepare photons of six non-orthogonal polarization states, and transmits them through the optical fiber Transmission to the receiving party, the receiving party uses a six-state quantum decoder to randomly generate six non-orthogonal polarization state measurement bases, and detects the six non-orthogonal polarization state photons sent by the sender. When the photon is detected, Send the measurement base used to the sender through the public channel, the sender tells the receiver that the measurement bases are selected correctly, and then the sender and the receiver keep the corresponding bits when the base is consistent, discard other data, and the receiver publishes some bits at will , for the sender to confirm whether there is any error. Finally, after the sender confirms that there is no error and no one is eavesdropping, the remaining bit sequence is reserved as the codebook.

范围内进行微调，ΔV为补偿电压，使右旋或左旋椭圆偏振光准确恢复成45°线偏振态的光子，实现退偏振的补偿。The quantum encoder and decoder of the phase modulation polarization state are used for polarization compensation: when the photon of the 45° linear polarization state sent by the sender becomes right-handed or Left-handed elliptically polarized light, at this time, the receiver can change the input voltage of the phase modulator to make it in

Fine-tuning within the range, ΔV is the compensation voltage, so that right-handed or left-handed elliptically polarized light can be accurately restored to photons in a 45° linear polarization state, and compensation for depolarization can be achieved.

Polarization compensation is performed by phase modulation polarization state, which effectively reduces the error rate. Because the polarization state of light is inevitably affected by the stress birefringence and polarization mode dispersion in the fiber and the environment during transmission, depolarization occurs, resulting in bit errors. Therefore, it is necessary to use polarization compensation technology for deflection correction.

In order to achieve more accurate compensation for the polarization state of light using the phase modulation polarization state method, the more specific method for polarization compensation of the phase modulation polarization state quantum encoder and decoder is as follows: the sender sends a standard 45° The linearly polarized photons are given to the receiving party, and the receiving party uses a 135° linear polarization measurement base to detect (according to Table 1, V ₁ =V ₀ /2, V ₂ =V ₀ /2, this measurement base can be produced), if The polarization state of the photon does not change during transmission, so the receiver cannot measure the photon. If the photon depolarizes during the transmission and becomes right-handed elliptically polarized light, then the receiver can measure the photon. At this time, the receiver only needs to change the voltage of V ₁ so that it is at Fine-tuning is performed within the range until no photons are measured at all, so that the photons return to the standard 45° linear polarization state.

Similarly, if the sender sends a standard right circularly polarized photon to the receiver, the receiver uses the left circular polarization measurement base to detect (according to Table 1, V ₁ =V ₀ /2, V ₂ =V ₀ , This kind of measurement basis is generated), in the case of no depolarization, the receiving party cannot measure the photon, if the photon depolarization occurs during the transmission, the receiving party can measure the photon, at this time, the receiving party only needs to change V ₁ voltage so that the Fine-tuning is performed within the range until no photons are measured at all, so that the photons return to the standard right-circular polarization state. Because this polarization compensation technology is realized by voltage modulation phase method, the compensation accuracy is very high, and the degree of polarization can reach 10 ^-5 , that is to say, the bit error rate caused by depolarization during transmission can be controlled at 10 ^-5

Compared with the prior art, the present invention has the following advantages:

(1) With the six-state quantum encoder and decoder we invented, the quantum cryptography communication of six-state encoding was realized experimentally for the first time, and, with the four-state quantum encoder and decoder we invented, the "two Quantum cryptography communication of BB84 protocol with linear polarization state plus two circular polarization states” 4-state encoding;

(2) Polarization modulation is carried out by the method of phase modulation polarization state, and the modulation voltage is low, only needing 0-10 volts, while using electro-optic crystals for polarization modulation, the half-wave voltage needs several thousand volts;

(3) The method of phase modulation polarization state is used for encoding and decoding, which can perform high-precision polarization compensation and effectively reduce the bit error rate.

Description of drawings

Fig. 1 is phase of the present invention--block diagram of polarization controller;

Among them: 1, 6-polarization beam splitter, 2, 3, 5-polarization maintaining fiber, 4-phase modulator.

Fig. 2 is the block diagram of four-state quantum encoder of the present invention;

Among them: 1, 6-polarization beam splitter, 2, 3, 5-polarization maintaining fiber, 4-phase modulator, 7-true random generator.

Fig. 3 is a four-state quantum cryptography communication circuit block diagram of the present invention;

Among them: 1, 6-polarization beam splitter, 2, 3, 5-polarization maintaining fiber, 4-phase modulator, 7-true random generator, 8-transmission fiber.

Fig. 4 is the block diagram of six-state quantum encoder of the present invention;

Among them: 1, 6-polarization beam splitter, 11, 16-polarization beam splitter after the polarization direction is rotated by 45°, 2, 3, 5, 12, 13, 15-polarization maintaining fiber, 4, 14-phase modulator , 7, 9-true random generator, 8-trigger, 10-single-mode fiber.

Fig. 5 is the block diagram of six-state quantum cipher communication circuit of the present invention;

Among them: 1, 6-polarization beam splitter, 11, 16-polarization beam splitter after the polarization direction is rotated by 45°, 2, 3, 5, 12, 13, 15-polarization maintaining fiber, 4, 14-phase modulator , 7, 9-true random generator, 8-trigger, 10-single-mode fiber, 17-transmission fiber

Detailed ways

Embodiment 1: Carry out quantum cryptography communication of BB84 protocol with four-state quantum encoder and decoder

For the first time, we have experimentally realized the quantum cryptography communication of the BB84 protocol using the 4-state encoding method of "two linear polarization states plus two circular polarization states". The optical path is shown in Figure 3, and the method is as follows: the sender uses a four-state quantum encoder to randomly prepare photons in four non-orthogonal polarization states, and transmits them to the receiver through an optical fiber, and the receiver uses a four-state quantum decoder to randomly generate four A set of non-orthogonal polarization state measurement bases detects the four non-orthogonal polarization state photons sent by the sender. In the case of detecting photons, the receiver sends the used measurement base to the sender through a public channel, and the sender Tell the receiver that the measurement bases are selected correctly, and then the sender and the receiver retain the corresponding bits when the measurement bases are consistent, and discard other data. The receiver publishes some bits at random for the sender to confirm whether there is an error, and finally the sender confirms After it is correct and it can be determined that no one is eavesdropping, the remaining bit sequence is reserved as the codebook.

Embodiment 2: Use a six-state quantum encoder and a decoder to perform six-state encoded quantum cryptography communication.

For the first time, we used six-state encoding to carry out six-state quantum cryptography communication. The optical path is shown in Figure 5. The sender uses a six-state quantum encoder to randomly prepare photons of six non-orthogonal polarization states, and transmits them to the receiver through an optical fiber. The receiver uses a six-state quantum decoder to randomly generate six non-orthogonal polarization state measurement bases, and detects the six non-orthogonal polarization state photons sent by the sender. The measurement base is sent to the sender through the public channel, and the sender tells the receiver that those measurement bases are selected correctly, and then the sender and the receiver keep the corresponding bits when the measurement base is consistent, and discard other data. The sender confirms whether there is any error, and finally after the sender confirms that there is no error and no one is eavesdropping, the remaining bit sequence is reserved as the codebook.

Embodiment 3: Polarization Compensation by Phase Modulation of Polarization State

范围内进行微调，直到完全测量不到光子为止，这样，光子就恢复成标准的右圆偏振态。由于这种偏振补偿技术是采用电压调制位相方法来实现，补偿的精度非常高，偏振度可以达到10^-5，也就是说，由传输过程中的退偏振所引起的误码率可以控制在10^-5以下。For the first time, we conducted polarization compensation experiments on the communication lines shown in Figure 4 and Figure 5 by phase-modulating the polarization state. The method is as follows: the sender sends a standard 45° linearly polarized Polarization measurement basis for detection (according to Table 1, V ₁ =V ₀ /2, V ₂ =V ₀ /2, this measurement basis can be generated), if the polarization state of the photon does not change during transmission, then the receiving If the photon is depolarized during transmission, for example, becomes right-handed elliptically polarized light, then the receiver may measure the photon. At this time, the receiver only needs to change the voltage of V ₁ to make Its Fine-tuning is performed within the range until no photons are measured at all, so that the photons return to the standard 45° linear polarization state. Similarly, if the sender sends a standard right circularly polarized photon to the receiver, the receiver uses the left circular polarization measurement base to detect (according to Table 1, V ₁ =V ₀ /2, V ₂ =V ₀ , This kind of measurement basis is generated), in the case of no depolarization, the receiver cannot measure the photon, if the photon is depolarized during transmission, the receiver may measure the photon, at this time, the receiver only needs to change V ₁ voltage so that the

Fine-tuning is performed within the range until no photons are measured at all, so that the photons return to the standard right-circular polarization state. Because this polarization compensation technology is realized by voltage modulation phase method, the compensation accuracy is very high, and the degree of polarization can reach 10 ^-5 , that is to say, the bit error rate caused by depolarization during transmission can be controlled at 10 ^-5 or less.

Claims (6)

1, a kind of four attitude quantum coding devices is characterized in that by a position phase--Polarization Controller and a true random generator are formed, and its light path is as follows: when the position phase--, and the input voltage of the phase modulator (4) in the Polarization Controller is respectively: 0, V ₀/ 2, V ₀, 3V ₀During/2 volts of four kinds of voltages, V ₀It is half-wave voltage, phase modulator (4) produces respectively: 0, the phase change of pi/2, π, 3 pi/2s, therefore, the position phase--Polarization Controller output polarization state of light is respectively: 45 ° of linear polarizations, right-hand circular polarization, 135 ° of linear polarizations, four kinds of nonopiate polarization states of Left-hand circular polarization; The input voltage of phase modulator (4) is provided by true random generator (7), and true random generator (7) can produce randomly: 0, V ₀/ 2, V ₀, 3V ₀/ 2 volts of four kinds of output voltages.

2, four attitude quantum coding devices according to claim 1, it is characterized in that a phase--Polarization Controller is by polarization beam apparatus, phase modulator and polarization maintaining optical fibre are formed, its light path is as follows: a branch of linearly polarized light incides first polarization beam apparatus (1), be divided into two bundle orthogonal linearly polarized light I in polarization direction and II, light beam I is through first polarization maintaining optical fibre (2), phase modulator (4) and the 3rd polarization maintaining optical fibre (5) enter second polarization beam apparatus (6), light beam II enters second polarization beam apparatus (6) through second polarization maintaining optical fibre (3), when the light path of light beam I and light beam II satisfies: n ₁L ₃=n ₁L ₂+ n ₁L ₅+ n ₂L ₄The time, light beam I and light beam II locate to take place polarization interference at second polarization beam apparatus (6), and its output polarization state of light is by the phasic difference decision of this two-beam, and the size of phasic difference is by phase modulator (4) control, described n ₁, n ₂Be respectively the refractive index of polarization maintaining optical fibre and phase modulator, L ₂, L ₃, L ₅Be respectively the length of first polarization maintaining optical fibre (2), second polarization maintaining optical fibre (3), the 3rd polarization maintaining optical fibre (5), L ₁Length for phase modulator (4); When the input voltage of phase modulator (4) respectively from 0 to 2V ₀When volt changed continuously, phase modulator (4) produced the phase change of from 0 to 2 π, described V ₀Be half-wave voltage; Therefore, export accordingly that polarization state of light can----Left-hand circular polarization changes right-hand circular polarization-135 ° linear polarization--left-handed elliptical polarization--right-handed elliptical polarization continuously from 45 ° of linear polarizations.

3, a kind of four attitude quantum decoders, it is characterized in that by a position phase--Polarization Controller and a true random generator are formed, be used for producing randomly four groups of nonopiate measuring polarization state bases, and measure base with these four groups and four kinds of nonopiate polarization state photons are detected and decode, these four groups nonopiate measuring polarization state bases are respectively: 45 ° of linear polarizations, right-hand circular polarization, 135 ° of linear polarizations, Left-hand circular polarization, they correspond respectively to the input voltage of phase modulator (4): 0, V ₀/ 2, V ₀, 3V ₀/ 2 volts, described V ₀Be half-wave voltage.

4, a kind of polarization compensation method that four attitude quantum coding devices and four attitude quantum decoders is used for quantum secret communication, wherein said four attitude quantum coding devices are four attitude quantum coding devices as claimed in claim 1, described four attitude quantum decoders are four attitude quantum decoders as claimed in claim 3, the photon that it is characterized in that 45 ° of linear polarization sending when transmit leg in transmission course owing to the influence that is subjected to the stress birfringence in the optical fiber becomes dextrorotation or left-handed elliptically polarized light, at this moment, the recipient can be by changing the input voltage of phase modulator, make its

Finely tune described V in the scope ₀Be half-wave voltage, Δ V is a bucking voltage, makes dextrorotation or left-handed elliptically polarized light accurately recover the photon of linear polarization at 45, realizes the compensation that depolarization is shaken.

5, method according to claim 4,45 ° of linear polarization photons that it is characterized in that a standard of transmit leg transmission are to the recipient, and the recipient measures bases with 135 ° of linear polarizations and detects, if photon its polarization state in transmission course does not change, so, the recipient just measures less than photon, shakes if depolarization takes place in transmission course photon, become elliptically polarized light, so, the recipient arrives photon with regard to energy measurement, at this moment, the recipient only need change the input voltage of its phase modulator, make its Finely tune in the scope, till measuring less than photon fully, photon just reverts to 45 ° of linear polarization of standard.

6, method according to claim 4, it is characterized in that transmit leg sends the right-hand circular polarization attitude photon of a standard to the recipient, the recipient measures base with left and detects, do not taking place under the situation that depolarization shakes, then the recipient just measures less than photon, shakes if depolarization takes place in transmission course photon, and the recipient arrives photon with regard to energy measurement, at this moment, the recipient only need change V ₁, V ₁Be the input voltage of phase modulator, make its Finely tune in the scope, till measuring less than photon fully, photon just reverts to the right-hand circular polarization attitude of standard.

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