Continuous-variable quantum teleportation method for propagating microwaves indoors

Abstract

This invention discloses a continuous-variable quantum teleportation method for propagating microwaves indoors, comprising the following steps: S1: At the sender's side, a two-mode squeezed state TMS is generated in a low-temperature environment using a Josephus parametric amplifier (JPA) and a microwave beam splitter, wherein the low-temperature environment refers to an absolute zero operating condition; and a state of the TMS is transferred to free space and transmitted to the receiver via a microwave transmitting antenna; S2: The sender measures the input state and a state of the TMS it possesses, generates a feedforward signal, and sends it to the receiver; S3: The receiver uses the received feedforward signal and the TMS state to obtain the input state to be transmitted, completing the quantum teleportation. This enables quantum communication in a real-world environment.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and in particular relates to a continuous variable quantum teleportation method for propagating microwaves indoors. Background Technology

[0002] Quantum teleportation (QT) allows for the achievement of what was traditionally impossible: transferring an unknown quantum state from one place to another without direct transmission. QT enables the intangible and secure transfer of unknown quantum states using quantum entanglement and classical communication as resources. It aims to transmit information about an unknown quantum state held by one party to a remote second party via entanglement resources and classical communication. QT was initially proposed for discrete-variable quantum states but has also been studied in continuous-variable settings. QT can be implemented based on either single-photon signals or continuous-variable signals. The former typically involves discrete quantum states, often using discrete qubits such as spin; achieving the former involves using discrete two-level systems like qubits, a technique called discrete-variable quantum teleportation (DVQT). The latter involves continuous-variable quantum states, typically described using continuous physical quantities such as position and momentum; achieving the latter may involve using quantum states with a continuous spectrum, such as the coherent state of a light field, a technique called continuous-variable quantum teleportation (CVQT).

[0003] Since continuous variables typically have infinite dimensions, CVQT possesses high-dimensional properties, potentially allowing the processing of high-dimensional information. Furthermore, in certain applications, CVQT may be more efficient in resource utilization. CVQT holds promise as a key technology supporting all-weather, long-distance quantum communication and has become a hot topic in current quantum secure communication technology research.

[0004] Experiments using CVQT at optical frequencies have proven feasible. Meanwhile, recent advances in quantum computing with superconducting circuits have spurred the need for quantum communication between spatially separated superconducting processors operating at microwave frequencies. This communication can be achieved by using propagated two-mode compressed (TMS) microwaves to entangle distant qubits, or by transmitting microwave states to interface between distant superconducting systems. Microwave CVQT shows great potential due to its inherent frequency and technological compatibility with superconducting quantum computers.

[0005] Therefore, there is an urgent need for a simple and effective continuous-variable quantum teleportation method for microwaves, which could make unconditionally secure microwave quantum communication possible. Summary of the Invention

[0006] The purpose of this invention is to provide a method for continuous variable quantum teleportation that propagates microwaves indoors, which solves the problem that traditional microwave quantum teleportation requires a harsh low-temperature environment and is closer to the quantum communication process under practical application conditions.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by this invention is a continuous variable quantum teleportation method for propagating microwaves indoors, comprising the following steps:

[0008] S1: A dual-mode compressed TMS is generated at a low temperature environment using a Joseph parametric amplifier (JPA) and a microwave beam splitter on the transmitter side. The low temperature environment refers to the operating condition with a temperature of 40 mK. One state of the TMS is then converted to free space and transmitted to the receiver via a microwave transmitting antenna.

[0009] S2: The sender measures the state of the input and a state of the TMS it possesses, generates a feedforward signal, and sends it to the receiver;

[0010] S3: The receiver uses the received feedforward signal and TMS state to obtain the state of the input to be transmitted, thus completing quantum teleportation.

[0011] Furthermore, S1 includes:

[0012] S1.1: In a low-temperature environment, two vacuum states are sent to two JPAs with the same compression energy level. These two JPAs are used with a local oscillator to compress the vacuum states, outputting two single-mode microwave compressed states; including:

[0013] S1.1.1: In a low-temperature environment, the JPA is used to generate a compressed state, and the output state of the JPA satisfies the following calculation formula:

[0014]

[0015] Wherein, the compression coefficient r satisfies:

[0016]

[0017] in, Indicates the output state of JPA. These represent the annihilation and generation operators of the light field input to JPA mode, respectively; cosh and sinh represent the hyperbolic cosine and hyperbolic sine functions, respectively; r represents the compression coefficient; g x g p These represent the gains of JPA in the position and momentum directions, respectively; e r represents the gain factor, and e represents the base of the natural logarithm;

[0018] S1.1.2: The dc SQUID is part of the JPA component, and the external pump frequency generated by the oscillating magnetic flux of the dc SQUID is f. pump The signal wave frequency is f signal ,

[0019] Satisfy f pump =2f signal DC SQUID is a phase-sensitive amplifier;

[0020] The phase-sensitive amplifier has two orthogonal modes. For each orthogonal mode, the relationship between gain and noise is as follows:

[0021]

[0022] Where η1 and η2 represent the noise of two orthogonal modes, respectively, G JPA1 G JPA2 These represent the gains of the two orthogonal modes, respectively.

[0023] Among them, G JPA1 G JPA2 When = 1, it is possible to generate two orthogonal single-mode compressed microwave states;

[0024] S1.2: The two orthogonal single-mode compressed microwave states obtained in S1.1 are combined on the first mixing ring to obtain a symmetrical dual-mode compressed microwave state; the first mixing ring is a beam splitter;

[0025] The matrix V corresponding to the symmetric dual-mode compressed microwave TMS obtained through the above process is represented as follows:

[0026]

[0027] Where I2 represents a 2×2 identity matrix, σ z Represented as 02 represents a 2×2 zero matrix, and a zero matrix is ​​represented as (0,0). T ;

[0028] S1.3: The transmitter in a low-temperature environment retains one state of the TMS, and uses a microwave transmitting antenna to transfer the other state of the TMS to free space and transmit it to the receiver; where,

[0029] The microwave transmitting antenna is a finite transmission line with variable impedance. One end of the transmission line is matched to the impedance of the low temperature environment, and the other end is matched to the impedance of the open air. At the same time, an exponential impedance profile structure is designed inside the antenna.

[0030] Furthermore, S2 includes:

[0031] S2.1: The sender combines the TMS state it possesses with the input state in the second mixing ring, which is a beam splitter;

[0032] S2.2: The output of the second mixing ring is directed to a pair of measurement JPAs, which perform strong phase-sensitive amplification with the same measurement gain and quadrature amplification angle;

[0033] S2.3: The output of the measured JPA is superimposed on the third mixing loop to obtain the feedforward signal; the third mixing loop is a beam splitter.

[0034] The output matrix B of the beam splitter is represented as:

[0035]

[0036] Where B represents the output matrix of the beam splitter, I2 represents the 2×2 identity matrix, O2 is a 2×2 zero matrix, and the zero matrix is ​​(0,0). T ;

[0037] The output matrices of the two measurements JPA are represented as follows:

[0038]

[0039]

[0040] Where G is the degeneracy gain of the two JPAs, and J3 and J4 represent the output matrices of the two measurement JPAs, respectively;

[0041] Considering the roles of the beam splitter and the two JPAs, the process matrix J is represented as:

[0042]

[0043] S2.4: Send the feedforward signal to the receiver, including:

[0044] When the sender transmits the feedforward signal, it still needs to couple the microwave state of the feedforward signal from the low-temperature environment to the open-air environment through the microwave transmitting antenna and send it to the receiver; the structure of the microwave transmitting antenna here is the same as that of the microwave transmitting antenna in S1.3.

[0045] Furthermore, S3 includes:

[0046] S3.1: After receiving the feedforward signal, the receiver converts the feedforward signal to a low-temperature environment through a microwave receiving antenna;

[0047] The microwave receiving antenna is a finite transmission line with variable impedance. One end of the transmission line is matched to the impedance of open air, and the other end is matched to the impedance of a low-temperature environment. At the same time, an exponential impedance profile structure is designed and implemented inside the antenna.

[0048] S3.2: The receiver converts the received TMS state to a low-temperature environment through a microwave receiving antenna;

[0049] The same microwave receiving antenna as in S3.1 is used here;

[0050] S3.3: In a low-temperature environment, the feedforward signal and TMS status are input into the directional coupler, and the desired state is obtained at the output of the directional coupler;

[0051] The output matrix of the directional coupler is represented as C:

[0052]

[0053] Where β is the coupling coefficient of the directional coupler, I2 represents the 2×2 identity matrix, 02 is the 2×2 zero matrix, and the zero matrix is ​​(0,0). T .

[0054] Furthermore, the stealth transfer processes in S2 and S3 are represented by matrix T as follows:

[0055]

[0056] Wherein, CBJ'B indicates that the stealth transmission process sequentially goes through: beam splitter, measurement JPA, beam splitter, and directional coupling process;

[0057] C represents the output matrix of the directional coupler, B represents the output matrix of the beam splitter, and J' represents the output matrix of the measured JPA, namely J3 and J4.

[0058] The beneficial effects of this invention are:

[0059] First, the method of this invention distributes compressed entangled states in free space. Compared with the traditional microwave quantum teleportation, which requires stringent experimental conditions in a low-temperature environment, it is closer to the actual quantum communication process and can better realize quantum communication in real-world environments.

[0060] Meanwhile, microwave signals have longer wavelengths and lower frequencies than optical signals. When microwave signals are transmitted through the air, they have lower absorption loss and energy consumption compared to existing optical signals. Compared to existing methods of using optical signals for continuous variable teleportation, the method of this invention has less attenuation and is more advantageous for short-distance transmission.

[0061] Furthermore, the method of this invention has lower costs and can provide technical support for the future development of quantum communication. Attached Figure Description

[0062] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0063] Figure 1 This is a flowchart of the method of the present invention.

[0064] Figure 2 A schematic diagram of the JPA architecture driven by component throughput.

[0065] Figure 3 This is a flowchart of the method of the present invention.

[0066] Figure 4 This describes the relationship between fidelity and transmission distance under specific conditions in the method of this invention. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] See Figures 1-3 The complete steps of the method of the present invention are as follows:

[0069] S1: A dual-mode compressed TMS is generated at low temperature using a Josephson parametric amplifier (JPA) and a microwave beam splitter on Alice's side. One state of the TMS is then transferred to free space via a microwave antenna and sent to Bob. The specific steps are described below:

[0070] S1.1: Two vacuum states are sent to two JPAs with identical compression energy levels in a cryogenic environment. The cryogenic environment refers to operating conditions close to absolute zero (0K), currently reaching 40mK. The input signal is compressed using these two JPAs and a local oscillator, outputting two single-mode compressed states. The specific steps are described below:

[0071] S1.1.1: Under low-temperature conditions, a squeezed state is generated using a flux-driven JPA, where the JPA is a coplanar waveguide resonator line terminated by a DC superconducting quantum interference device (dc SQUID). The calculation formula for the output state of the JPA is as follows:

[0072]

[0073] Wherein, the compression coefficient r satisfies:

[0074]

[0075] in, Indicates the output state of JPA. These represent the annihilation and generation operators of the light field input to JPA mode, respectively; cosh and sinh represent the hyperbolic cosine and hyperbolic sine functions, respectively; r represents the compression coefficient; g x g p These represent the amplifier's gain in the position and momentum directions, respectively; e r represents the gain factor, and e represents the base of the natural logarithm;

[0076] S1.1.2: The dc SQUID, as part of the JPA component, provides magnetic flux tunability for the resonator and enables parametric phase-sensitive amplification, which is crucial for generating compressed microwave states. The external pump frequency generated by the oscillating magnetic flux of the dc SQUID is f. pump The signal wave frequency is f signal ,

[0077] When f pump =2f signal At this time, the DC SQUID is called a phase-sensitive amplifier (or degenerate amplifier);

[0078] When f pump ≠2f signal When dc SQUID is used, it is called a phase-insensitive amplifier (or non-degenerate amplifier).

[0079] This embodiment uses a phase-sensitive amplifier. A phase-sensitive amplifier can compress one canonical component while simultaneously decompressing another. The phase-sensitive amplifier has two orthogonal modes i. For each orthogonal mode i, the gain G... JPAi and noise η i The relationship for i∈{1,2} is as follows:

[0080]

[0081] Where η1 and η2 represent the noise of two orthogonal modes, respectively, G JPA1 G JPA2 These represent the gains of the two orthogonal modes, respectively.

[0082] When G is satisfied JPA1 G JPA2 When = 1, noiseless amplification can be achieved, that is, the generation of single-mode compressed microwave state is completed.

[0083] S1.2: The two orthogonal single-mode compressed states obtained in S1.1 are combined on the first mixing ring to obtain a symmetrical two-mode compressed state. The first mixing ring is a 50:50 microwave beam splitter.

[0084] The matrix V corresponding to the symmetric dual-mode compressed TMS prepared through the above process is represented as follows:

[0085]

[0086] Where I2 represents a 2×2 identity matrix, σ z It is one of the Pauil matrices, and its form is 02 represents a 2×2 zero matrix, and a zero matrix represents (0,0). T ;

[0087] S1.3: Alice, in a cryogenic environment, retains one state of the TMS and sends the other state of the TMS to Bob in free space. To send the microwave state generated in the cryogenic environment to Bob, a microwave antenna is used as an interface to couple one state of the TMS from the cryogenic environment to free space. The interface microwave antenna acts as a non-uniform medium, connecting the cryogenic environment and free space, and then sending this state to Bob through free space. Details are as follows:

[0088] The main purpose of a microwave antenna that couples a cryogenic environment to free space is to maximize the transmission of the incident signal into the open medium. Therefore, it is necessary to minimize signal loss and reflection during the transition from the transmission line (impedance of approximately 50Ω) in the cryogenic environment to free space (impedance of approximately 377Ω).

[0089] To effectively transmit microwave signals from a cryogenic system to open-air air, the impedance mismatch between the two needs to be addressed. To this end, a finite transmission line with variable characteristic impedance is used as a transition, allowing one end of the transmission line to match the 50Ω impedance of the cryogenic environment, while the other end matches the 377Ω impedance of open-air air.

[0090] By cleverly designing and implementing an exponential impedance profile structure inside the antenna, the antenna's reflectivity can be significantly reduced to below 10. -9 This level of performance is comparable to that of traditional high-efficiency horn antennas, ensuring extremely low loss and high-efficiency radiation output of microwave signals.

[0091] S2: On Alice's side, the input state and a state of Alice's TMS are measured, a feedforward signal is generated, and sent to Bob. The specific steps are described below:

[0092] S2.1: Alice combines the TMS state she possesses with the input state in a second mixing loop, which is a 50:50 microwave beam splitter.

[0093] S2.2: The output of the second mixing ring is directed to a pair of measurement JPAs, which perform strong phase-sensitive amplification with the same measurement gain and quadrature amplification angle.

[0094] S2.3: The output of the measured JPA is superimposed on the third mixing loop to obtain the feedforward signal. The third mixing loop is a 50:50 microwave beam splitter.

[0095] The 50:50 beam splitters on Alice's side are all represented as:

[0096]

[0097] Where B represents the output matrix of the beam splitter, I2 represents the 2×2 identity matrix, O2 is a 2×2 zero matrix, and the zero matrix is ​​(0,0). T .

[0098] The phase-sensitive amplification of JPA measurement is expressed as:

[0099]

[0100] Where G is the degeneracy gain of the two JPAs, and J3 and J4 represent the output matrices of the two measurement JPAs, respectively.

[0101] Considering the roles of the beam splitter and the two JPAs, the process matrix J is represented as:

[0102]

[0103] S2.4: Send the feedforward signal to Bob's side. Details are as follows:

[0104] When Alice sends the feedforward signal, she still needs to couple the microwave state of the feedforward signal from the low-temperature environment to the open-air environment through a microwave antenna, and then send it to Bob through an indoor quantum channel. Here, the microwave antenna has the same structure and function as the microwave antenna in S1.3.

[0105] S3: Using the received feedforward signal and TMS state on Bob's side, the desired input state is obtained, completing quantum teleportation. The specific steps are as follows:

[0106] S3.1: After receiving the feedforward signal sent by Alice, Bob's side uses a microwave antenna to switch it to a low-temperature environment.

[0107] The receiving antenna is the same as the transmitting antenna, and is simulated by a transmission line with varying spatial impedance. A finite transmission line with variable characteristic impedance is used as a transition, so that one end of the transmission line can match the 377Ω impedance of open air, and the other end can match the 50Ω impedance of low temperature environment, thereby realizing the connection between open air channel and low temperature environment.

[0108] S3.2: Bob's side will transfer the TMS state received from Alice to a low-temperature environment via a microwave antenna.

[0109] The same receiving antenna as in S3.1 is used here.

[0110] S3.3: In a low-temperature environment, the feedforward signal and the TMS state are input into a directional coupler with a coupling constant of β, and the desired state is obtained at the output of the directional coupler.

[0111] The output matrix of the directional coupler is represented as C:

[0112]

[0113] Where β is the coupling coefficient of the directional coupler, I2 represents the 2×2 identity matrix, 02 is the 2×2 zero matrix, and the zero matrix is ​​(0,0). T .

[0114] The stealth transfer method following the above S2 and S3 processes can be represented by matrix T as follows:

[0115]

[0116] In this context, CBJB indicates that the stealth transmission process sequentially undergoes a mixing loop (microwave beam splitter) process, a measurement JPA process, another mixing loop (microwave beam splitter) process, and a displacement operation process performed by the directional coupler.

[0117] C is the matrix representation of the directional coupler, B is the matrix representation of the beam splitter, and J' is the matrix representation of the measured JPA (representing processes J3 and J4).

[0118] The inventive point of this invention:

[0119] Compared to existing microwave quantum teleportation processes that can only be carried out in low-temperature environments, the invention of this invention lies in introducing a microwave antenna into the microwave quantum teleportation process, thereby realizing the distribution of microwave entangled states in an open-air environment.

[0120] The beneficial effects of this invention are:

[0121] First, the method of this invention distributes compressed entangled states in free space. Compared with the traditional microwave quantum teleportation which requires stringent experimental conditions in a low-temperature environment, the experimental conditions of the method of this invention are simpler and closer to the actual quantum communication process, thus enabling better quantum communication in real-world environments.

[0122] Meanwhile, microwave signals have longer wavelengths and lower frequencies than optical signals. When microwave signals are transmitted through the air, they have lower absorption loss and energy consumption compared to existing optical signals. Compared to existing methods of using optical signals for continuous variable teleportation, the method of this invention has less attenuation and is more advantageous for short-distance transmission.

[0123] Furthermore, the method of this invention can reduce costs to a certain extent and provide technical support for the future development of quantum communication, potentially having a positive impact on microwave quantum communication.

[0124] (1) The loss of microwave signals during transmission in open-air environments mainly includes path loss and absorption loss. Path loss refers to the attenuation of the signal during propagation in free space, and its magnitude is proportional to the transmission distance. According to Fries's transmission formula, which describes the propagation loss of signals in free space, the loss is related to the transmission distance and the carrier frequency. Specifically, the loss is proportional to the square of the distance and the square of the frequency. Therefore, the higher the frequency, the greater the loss, meaning that optical waves have greater loss than microwaves when transmitted in the same free space. Absorption loss is the loss caused by the absorption and scattering of microwave signals by molecules such as water vapor, oxygen, and nitrogen in the atmosphere during signal transmission, resulting in a decrease in signal power as the distance increases. Microwaves have less absorption loss when transmitted in free space compared to optical waves, mainly because of their different propagation characteristics in the atmosphere. Microwaves have lower frequencies and longer wavelengths, so their energy diffusion loss in free space is relatively small. Optical waves (such as visible light) have higher frequencies and shorter wavelengths, making them more easily absorbed by molecules and particles in the atmosphere, resulting in greater loss. Atmospheric absorption also has different effects on electromagnetic waves of different frequencies. For example, water vapor and oxygen molecules produce absorption peaks for electromagnetic waves at specific frequencies, which are typically higher than the microwave frequency band. Therefore, under the same conditions, the atmospheric absorption loss of microwaves is generally less than that of optical frequencies.

[0125] In summary, due to the low frequency of microwaves, their path loss is low according to the Friesian propagation formula; at the same time, due to the low frequency and long wavelength, microwaves are not easily absorbed by atmospheric molecules, so the propagation loss of microwaves in free space is small.

[0126] (2) The formula for calculating the gain of a microwave antenna is:

[0127]

[0128] Where G is the antenna gain, A is the effective area of ​​the antenna, D is the antenna diameter, η is the antenna efficiency, which is generally between 0.5 and 0.7, and λ is the wavelength of the signal.

[0129] Assuming a 5 GHz microwave propagates 50 m in an ideal dry environment, the signal wavelength λ = c / f = 6 × 10⁻⁶ m. -2 Given m, a transmission distance d = 50m, then:

[0130] Path loss L p =20log10(4πd / λ) =20log 10 (4πd / λ)≈80dB

[0131] Absorption loss L a =γmw×d=6.26×10 -3 dB / km × 50 / 1000km ≈ 3.13 × 10 -4 dB

[0132] Assuming the antenna diameter is 3m and the antenna efficiency η = 0.6,

[0133] That is, the transmitting antenna gain G t =Receive antenna gain

[0134] G t +G r -L p -L a A gain >0 indicates that the gain of the transmitting and receiving antennas can compensate for the transmission loss in open-air environments.

[0135] Therefore, the gain of the transmitting and receiving microwave antennas can compensate for the path loss and absorption loss when the signal is transmitted in the open environment. In other words, the method proposed in this scheme can realize the entanglement distribution and teleportation of microwaves in free space.

[0136] (3) See Figure 4 After adopting the entanglement distribution in the open-air environment described in this method, assuming a compression factor r of 1, the microwave antenna is a perfect antenna (i.e., the antenna's reflectivity η). ant =0, in fact, the reflectivity of current microwave antennas can reach 10. -9 Below, for ease of calculation, the relationship between the fidelity of the quantum teleportation process and the distance that the microwave entangled state can transmit before complete degeneration is as follows (assuming the antenna reflectivity is set to 0 and the optimal measurement gain is 21dB). Figure 4 As shown.

[0137] like Figure 4It can be seen that, under optimal gain conditions, the longest transmission distance over which the asymmetric microwave entangled state used in this scheme can maintain its quantum nature in an open-air environment is 434m. That is, the microwave state can retain its quantum nature after transmission over 434m, thus this method can extend microwave quantum teleportation to free space. This research result is of great significance for extending quantum communication to larger-scale free space, especially for realizing practical quantum communication networks in the microwave frequency band.

[0138] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0139] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A continuous-variable quantum teleportation method for propagating microwaves indoors, characterized in that, Includes the following steps: S1: A dual-mode compressed TMS is generated at a low temperature environment using a Joseph parametric amplifier (JPA) and a microwave beam splitter on the transmitter side. The low temperature environment refers to the operating condition with a temperature of 40 mK. One state of the TMS is then converted to free space and transmitted to the receiver via a microwave transmitting antenna. S2: The sender measures the state of the input and a state of the TMS it possesses, generates a feedforward signal, and sends it to the receiver; S3: The receiver uses the received feedforward signal and TMS state to obtain the state of the input to be transmitted, thus completing quantum teleportation.

2. The continuous-variable quantum teleportation method for propagating microwaves indoors according to claim 1, characterized in that, S1 includes: S1.1: In a low-temperature environment, two vacuum states are sent to two JPAs with the same compression energy level. These two JPAs are used with a local oscillator to compress the vacuum states, outputting two single-mode microwave compressed states; including: S1.1.1: In a low-temperature environment, the JPA is used to generate a compressed state, and the output state of the JPA satisfies the following calculation formula: Wherein, the compression coefficient r satisfies: in, Indicates the output state of JPA. These represent the annihilation and generation operators of the light field input to JPA mode, respectively; cosh and sinh represent the hyperbolic cosine and hyperbolic sine functions, respectively; r represents the compression coefficient; g x g p These represent the gains of JPA in the position and momentum directions, respectively; e r represents the gain factor, and e represents the base of the natural logarithm; S1.1.2: The dc SQUID is part of the JPA component, and the external pump frequency generated by the oscillating magnetic flux of the dc SQUID is f. pump The signal wave frequency is f signal , Satisfy f pump =2f signal DC SQUID is a phase-sensitive amplifier; The phase-sensitive amplifier has two orthogonal modes. For each orthogonal mode, the relationship between gain and noise is as follows: Where η1 and η2 represent the noise of two orthogonal modes, respectively, G JPA1 G JPA2 These represent the gains of the two orthogonal modes, respectively. Among them, G JPA1 G JPA2 When = 1, it is possible to generate two orthogonal single-mode compressed microwave states; S1.2: The two orthogonal single-mode compressed microwave states obtained in S1.1 are combined on the first mixing ring to obtain a symmetrical dual-mode compressed microwave state; the first mixing ring is a beam splitter; The matrix V corresponding to the symmetric dual-mode compressed microwave TMS obtained through the above process is represented as follows: Where I2 represents a 2×2 identity matrix, σ z Represented as 02 represents a 2×2 zero matrix, and a zero matrix is ​​represented as (0,0). T ; S1.3: The transmitter in a low-temperature environment retains one state of the TMS, and uses a microwave transmitting antenna to transfer the other state of the TMS to free space and transmit it to the receiver; where, The microwave transmitting antenna is a finite transmission line with variable impedance. One end of the transmission line is matched to the impedance of the low temperature environment, and the other end is matched to the impedance of the open air. At the same time, an exponential impedance profile structure is designed inside the antenna.

3. The continuous-variable quantum teleportation method for propagating microwaves indoors according to claim 2, characterized in that, S2 includes: S2.1: The sender combines the TMS state it possesses with the input state in the second mixing ring, which is a beam splitter; S2.2: The output of the second mixing ring is directed to a pair of measurement JPAs, which perform strong phase-sensitive amplification with the same measurement gain and quadrature amplification angle; S2.3: The output of the measured JPA is superimposed on the third mixing loop to obtain the feedforward signal; the third mixing loop is a beam splitter. The output matrix B of the beam splitter is represented as: Where B represents the output matrix of the beam splitter, I2 represents the 2×2 identity matrix, O2 is a 2×2 zero matrix, and the zero matrix is ​​(0,0). T ; The output matrices of the two measurements JPA are represented as follows: Where G is the degeneracy gain of the two JPAs, and J3 and J4 represent the output matrices of the two measurement JPAs, respectively; Considering the roles of the beam splitter and the two JPAs, the process matrix J is represented as: S2.4: Send the feedforward signal to the receiver, including: When the sender transmits the feedforward signal, it still needs to couple the microwave state of the feedforward signal from the low-temperature environment to the open-air environment through the microwave transmitting antenna and send it to the receiver; the structure of the microwave transmitting antenna here is the same as that of the microwave transmitting antenna in S1.

3.

4. The continuous-variable quantum teleportation method for propagating microwaves indoors according to claim 3, characterized in that, S3 includes: S3.1: After receiving the feedforward signal, the receiver converts the feedforward signal to a low-temperature environment through a microwave receiving antenna; The microwave receiving antenna is a finite transmission line with variable impedance. One end of the transmission line is matched to the impedance of open air, and the other end is matched to the impedance of a low-temperature environment. At the same time, an exponential impedance profile structure is designed and implemented inside the antenna. S3.2: The receiver converts the received TMS state to a low-temperature environment through a microwave receiving antenna; The same microwave receiving antenna as in S3.1 is used here; S3.3: In a low-temperature environment, the feedforward signal and TMS status are input into the directional coupler, and the desired state is obtained at the output of the directional coupler; The output matrix of the directional coupler is represented as C: Where β is the coupling coefficient of the directional coupler, I2 represents the 2×2 identity matrix, 02 is the 2×2 zero matrix, and the zero matrix is ​​(0,0). T .

5. The continuous-variable quantum teleportation method for propagating microwaves indoors according to any one of claims 1, 3, and 4, characterized in that, The stealth transfer processes in S2 and S3 are represented by matrix T as follows: Wherein, CBJ'B indicates that the stealth transmission process sequentially goes through: beam splitter, measurement JPA, beam splitter, and directional coupling process; C represents the output matrix of the directional coupler, B represents the output matrix of the beam splitter, and J' represents the output matrix of the measured JPA, namely J3 and J4.

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