Direct detection gaussian modulation continuous variable quantum key distribution method and system
By directly probing the intensity of the optical signal and recovering the phase information using the Kramers-Kronig relation, the problem of complex receiver equipment is solved, and the Gaussian modulation continuous variable quantum key distribution system is simplified and its cost reduced.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANGHAI JIAOTONG UNIV
- Filing Date
- 2024-06-24
- Publication Date
- 2026-07-21
AI Technical Summary
In existing Gaussian modulation continuous variable quantum key distribution systems, the use of coherent detection methods by the receiver leads to complex and uneconomical equipment, which hinders the widespread application of the system.
A direct detection method is used to obtain the intensity information of the optical signal through a photodiode, and the phase information is recovered by using the Kramers-Kronig relationship, which simplifies the optical path structure and generates a security key.
The simplified receiver equipment reduced costs and enabled effective detection of Gaussian-modulated complex signals, promoting the widespread application of the system.
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Figure CN118784217B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the technical field of quantum key distribution, specifically to a Gaussian modulation continuous variable quantum key distribution method and system based on direct detection, and more particularly to a Gaussian modulation continuous variable quantum key distribution method based on direct detection of the Kramers-Kronig relation. Background Technology
[0002] The modern era is the information age, with information systems permeating every aspect of people's lives. However, information security issues arise constantly during information transmission, and the security threats are becoming increasingly serious, especially for sensitive information requiring confidentiality. Protecting this confidential information has garnered increasing attention. With the development of quantum computing technology, widely used traditional cryptographic systems, particularly those based on computational complexity, are increasingly threatened by ever-growing computing power. Therefore, researching information security solutions capable of preventing future attacks from quantum computers is essential.
[0003] Quantum cryptography is a crucial solution to this threat. It utilizes quantum physics principles such as the no-cloning theorem and the Heisenberg uncertainty principle to achieve information-theoretical security, rather than relying on high computational complexity. Therefore, its security remains unaffected by future increases in computing power. Quantum key distribution (QKD) is one of the most successful applications of quantum cryptography. Based on the laws of quantum physics, it distributes symmetric keys between a pair of legitimate parties, guaranteeing information-theoretical security. Combining quantum key distribution with a "one-time pad" system can ensure secure communication even as computing power continues to grow. Continuous-variable quantum key distribution is a type of quantum key distribution. Compared to discrete-variable quantum key distribution, it has gained widespread attention due to its compatibility with classical optical communication systems, readily available light sources, and simpler detection systems.
[0004] Among existing continuous-variable quantum key distribution (CVD) schemes, Gaussian modulation CVD, also known as the GG02 protocol, is widely used. Proposed by F. Grosshans and P. Granger in 2002, it primarily involves the sender modulating two sets of Gaussian-distributed random numbers onto two orthogonal components of an optical field. The receiver then detects these numbers and generates the key through post-processing. In practical CVD systems, the receiver often uses coherent detection to detect the orthogonal components of the received optical field. However, existing coherent detection systems have complex optical path structures and require a local oscillator, making the user-end equipment less economical and streamlined, thus hindering the widespread application of CVD.
[0005] Therefore, a new technical solution is needed to improve the above-mentioned technical problems. Summary of the Invention
[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a direct-probe Gaussian modulation continuous-variable quantum key distribution method and system.
[0007] According to the present invention, a direct-probe Gaussian-modulated continuous-variable quantum key distribution method is provided, the method comprising the following steps:
[0008] Step S1: The sender generates two sets of independent Gaussian distributed random numbers and uses them to generate a Gaussian modulated radio frequency signal. Then, it constructs a minimum phase signal by spectrum shifting and adding a DC component. The signal is used to modulate the light and transmit the optical signal through the optical fiber.
[0009] Step S2: The receiver uses a photodiode to detect the received coherent optical signal and obtain the intensity information of the optical signal;
[0010] Step S3: Apply the Kramers-Kronig relation to the obtained light intensity information to obtain its phase information, thereby recovering the original complex signal, and then obtaining the information loaded on the two canonical components. After reverse negotiation and security enhancement post-processing steps, the final security key is generated.
[0011] Preferably, step S1 includes the following steps:
[0012] Step S1.1: The sender generates two sets of independent Gaussian distributed random numbers, loads them onto a raised cosine pulse, and combines the two as the real and imaginary parts respectively to obtain a complex signal;
[0013] Step S1.2: Construct the above complex signal into a minimum phase signal by first shifting the spectrum of the original signal so that the left edge of its frequency band is at 0, and then adding a DC component;
[0014] Step S1.3: After loading the minimum phase signal, the real part and the imaginary part are loaded onto the I and Q paths of the IQ modulator respectively to modulate the light. The modulated optical signal is then transmitted through the optical fiber channel.
[0015] The continuous variable refers to a signal that takes continuously increasing values, as used in the key distribution system.
[0016] The direct detection refers to detecting the intensity information of the optical signal;
[0017] In step S2: the expression for the photocurrent I(t) measured by the photodiode is:
[0018] I(t)=E′(t)| 2=|E(t)| 2
[0019] Where t represents time.
[0020] Preferably, in step S1.1: two sets of Gaussian distributed random numbers are loaded onto a raised cosine pulse as complex signals with real and imaginary parts, the spectral width being B and the spectral range being [missing information]. arrive
[0021] In step S1.2: based on the original complex signal E s The expression for the minimum phase signal E(t) constructed by (t) is:
[0022] E(t)=E s (t)exp(iπBt)+E0
[0023] Where i is the imaginary unit, and the real constant E0 satisfies |E0|>|E s (t)|;
[0024] In step S1.3: the signal E′(t) obtained after loading the minimum phase signal E(t) with a wave is:
[0025] E′(t)=E(t)exp(i2πf c t)
[0026] Where f c For carrier frequency.
[0027] Preferably, step S3 includes the following steps:
[0028] Step S3.1: Apply the Kramers-Kronig relation to the received photocurrent signal I(t) to obtain the phase information of the minimum phase signal lost during direct detection. The phase information is obtained through Hilbert transform.
[0029] Step S3.2: The amplitude information of the minimum phase signal is obtained directly from the photocurrent signal, and the minimum phase signal can be recovered by combining it with the phase information;
[0030] Step S3.3: Obtain the original and complex signals based on the minimum phase signal. Perform the reverse operation during construction on the minimum phase signal recovered by the receiver to obtain the original and complex signals. First, remove the DC component, and then perform spectrum shifting to move the frequency band center back to the center frequency 0.
[0031] Step S3.4: The receiver extracts data from the recovered complex signal, performs reverse negotiation and confidentiality enhancement post-processing steps with the sender, and generates the final binary security key.
[0032] Preferably, the amplitude information A of the minimum phase informationE (t) is:
[0033]
[0034] Phase information φ recovered by Hilbert transform E (t) is:
[0035]
[0036] Where pv represents the Cauchy principal value;
[0037] The minimum phase signal E recovered by the receiver r (t) is:
[0038]
[0039] The receiver uses the minimum phase signal E r (t) yields the original complex signal E rs (t) is:
[0040] E rs (t)=(E r (t)-E r0 )exp(-iπBt);
[0041] Among them, due to the attenuation effect of the channel during transmission, the DC component E of the received signal... r0 The DC component E0 added during transmission is different from the DC component E0 added during transmission, so they cannot be directly subtracted. The mean of the real part of the minimum phase signal is taken as the DC component E of the received signal. r0 Value:
[0042]
[0043] Where real(x) represents taking the real part of x, and n is the number of data points.
[0044] The present invention also provides a direct-probe Gaussian-modulated continuous-variable quantum key distribution system, the system comprising the following modules:
[0045] Module M1: The transmitter generates two sets of independent Gaussian distributed random numbers, and uses them to generate a Gaussian modulated radio frequency signal. Then, through spectrum shifting and adding a DC component, it is constructed into a minimum phase signal. The signal is used to modulate the light and transmit the optical signal through the optical fiber.
[0046] Module M2: The receiver uses a photodiode to detect the received coherent optical signal and obtain the intensity information of the optical signal;
[0047] Module M3: Apply the Kramers-Kronig relation to the obtained light intensity information to obtain its phase information, thereby recovering the original complex signal, and then obtaining the information loaded on the two canonical components. After reverse negotiation and security enhancement post-processing modules, the final security key is generated.
[0048] Preferably, module M1 includes the following modules:
[0049] Module M1.1: The sender generates two sets of independent Gaussian distributed random numbers, loads them onto a raised cosine pulse, and combines the two as the real and imaginary parts respectively to obtain a complex signal;
[0050] Module M1.2: Construct the above complex signal into a minimum phase signal by first shifting the spectrum of the original signal so that the left edge of its frequency band is at 0, and then adding a DC component;
[0051] Module M1.3: After the minimum phase signal is loaded onto the wave, its real and imaginary parts are loaded onto the I and Q channels of the IQ modulator respectively to modulate the light. The modulated optical signal is then transmitted through the optical fiber channel.
[0052] The continuous variable refers to a signal that takes continuously increasing values, as used in the key distribution system.
[0053] The direct detection refers to detecting the intensity information of the optical signal;
[0054] In module M2, the expression for the photocurrent I(t) measured by the photodiode is:
[0055] I(t)=E′(t)| 2 =|E(t)| 2 .
[0056] Where t represents time.
[0057] Preferably, in module M1.1: two sets of Gaussian distributed random numbers are loaded onto a raised cosine pulse as complex signals with real and imaginary parts, the spectral width being B, and the spectral range being [missing information]. arrive
[0058] In module M1.2: based on the original complex signal E s The expression for the minimum phase signal E(t) constructed by (t) is:
[0059] E(t)=E s (t)exp(iπBt)+E0
[0060] Where i is the imaginary unit, and the real constant E0 satisfies |E0|>|E s (t)|;
[0061] In module M1.3: the signal E′(t) obtained after loading a wave onto the minimum phase signal E(t) is:
[0062] E′(t)=E(t)exp(i2πf c t)
[0063] Where f c For carrier frequency.
[0064] Preferably, module M3 includes the following modules:
[0065] Module M3.1: Apply the Kramers-Kronig relation to the received photocurrent signal I(t) to obtain the phase information of the minimum phase signal lost during direct detection. The phase information is obtained through Hilbert transform.
[0066] Module M3.2: The amplitude information of the minimum phase signal is obtained directly from the photocurrent signal, and the minimum phase signal can be recovered by combining it with the phase information;
[0067] Module M3.3: Obtain the original and complex signals based on the minimum phase signal. Perform the reverse operation during construction on the minimum phase signal recovered by the receiver to obtain the original and complex signals. First, remove the DC component, and then perform spectrum shifting to move the frequency band center back to the center frequency 0.
[0068] Module M3.4: The receiver extracts data from the recovered complex signal, performs reverse negotiation with the sender, and is a confidentiality enhancement post-processing module to generate the final binary security key.
[0069] Preferably, the amplitude information A of the minimum phase information E (t) is:
[0070]
[0071] Phase information φ recovered by Hilbert transform E (t) is:
[0072]
[0073] Where pv is the Cauchy principal value;
[0074] The minimum phase signal E recovered by the receiver r (t) is:
[0075]
[0076] The receiver uses the minimum phase signal E r (t) yields the original complex signal E rs (t) is:
[0077] Ers (t)=(E r (t)-E r0 )exp(-iπBt);
[0078] Among them, due to the attenuation effect of the channel during transmission, the DC component E of the received signal... r0 The DC component E0 added during transmission is different from the DC component E0 added during transmission, so they cannot be directly subtracted. The mean of the real part of the minimum phase signal is taken as the DC component E of the received signal. r0 Value:
[0079]
[0080] Where real(x) represents taking the real part of x, and n is the number of data points.
[0081] Compared with the prior art, the present invention has the following beneficial effects:
[0082] 1. This invention completes the coherent state reception step of a quantum key distribution system, thereby improving the problem that the coherent detection system used by the receiver in the traditional Gaussian modulation quantum key distribution scheme is too complex;
[0083] 2. The Gaussian modulation continuous variable quantum key distribution scheme provided by this invention changes the way the receiver detects optical signals. It uses photodiode direct detection instead of coherent detection, and recovers the phase information from the intensity information of the optical signal by applying the Kramers-Kronig relation, thereby realizing the detection of Gaussian modulation complex signals. This simplifies the optical path structure, reduces the cost of the receiver, and is conducive to the widespread application of continuous variable quantum key distribution systems. Attached Figure Description
[0084] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:
[0085] Figure 1 This is a diagram of a Gaussian-modulated continuous-variable quantum key distribution system based on direct detection of the Kramers-Kronig relation. Detailed Implementation
[0086] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.
[0087] Example 1:
[0088] Reference Figure 1 According to the present invention, a direct-probe Gaussian-modulated continuous-variable quantum key distribution method includes the following steps:
[0089] Step S1: The sender generates two sets of independent Gaussian distributed random numbers and uses them to generate a Gaussian modulated radio frequency signal. Then, it constructs a minimum phase signal by spectrum shifting and adding a DC component. The signal is used to modulate the light and transmit the optical signal through the optical fiber.
[0090] Step S1.1: The sender generates two sets of independent Gaussian distributed random numbers, loads them onto a raised cosine pulse, and combines the two as the real and imaginary parts respectively to obtain a complex signal;
[0091] Step S1.2: Construct the above complex signal into a minimum phase signal by first shifting the spectrum of the original signal so that the left edge of its frequency band is at 0, and then adding a DC component;
[0092] Step S1.3: After loading the minimum phase signal, the real part and the imaginary part are loaded onto the I and Q paths of the IQ modulator respectively to modulate the light. The modulated optical signal is then transmitted through the optical fiber channel.
[0093] The continuous variable refers to a signal that takes continuously increasing values, as used in the key distribution system.
[0094] The direct detection refers to detecting the intensity information of the optical signal;
[0095] Two sets of Gaussian distributed random numbers are loaded onto a raised cosine pulse to form a complex signal with real and imaginary parts. The signal's spectral width is B, and its spectral range is... arrive
[0096] According to the original signal E s The expression for the minimum phase signal E(t) constructed by (t) is:
[0097] E(t)=E s (t)exp(iπBt)+E0
[0098] Where t represents time, i is the imaginary unit, and the real constant E0 satisfies |E0|>|E s (t)|;
[0099] The signal E′(t) obtained after loading a wave onto the minimum-phase signal E(t) is:
[0100] E′(t)=E(t)exp(i2πf c t)
[0101] Where f c For carrier frequency.
[0102] Step S2: The receiver uses a photodiode to detect the received coherent optical signal and obtain the intensity information of the optical signal;
[0103] The expression for the photocurrent I(t) measured by the photodiode is:
[0104] I(t)=E′(t)| 2 =|E(t)| 2 .
[0105] Step S3: Apply the Kramers-Kronig relation to the obtained light intensity information to obtain its phase information, thereby recovering the original complex signal, and then obtaining the information loaded on the two canonical components. After reverse negotiation and security enhancement post-processing steps, the final security key is generated.
[0106] Step S3.1: Apply the Kramers-Kronig relation to the received photocurrent signal I(t) to obtain the phase information of the minimum phase signal lost during direct detection. The phase information is obtained through Hilbert transform.
[0107] Step S3.2: The amplitude information of the minimum phase signal is obtained directly from the photocurrent signal, and the minimum phase signal can be recovered by combining it with the phase information;
[0108] Step S3.3: Obtain the original and complex signals based on the minimum phase signal. Perform the reverse operation during construction on the minimum phase signal recovered by the receiver to obtain the original and complex signals. First, remove the DC component, and then perform spectrum shifting to move the frequency band center back to the center frequency 0.
[0109] Step S3.4: The receiver extracts data from the recovered complex signal, performs reverse negotiation and confidentiality enhancement post-processing steps with the sender, and generates the final binary security key.
[0110] Amplitude information A of minimum phase information E (t) is:
[0111]
[0112] Phase information φ recovered by Hilbert transform E (t) is:
[0113]
[0114] Where pv is the Cauchy principal value.
[0115] The minimum phase signal E recovered by the receiver r (t) is:
[0116]
[0117] The receiver uses the minimum phase signal E r (t) yields the original complex signal E rs (t) is:
[0118] E rs (t)=(E r (t)-E r0 )exp(-iπBt);
[0119] Among them, due to the attenuation effect of the channel during transmission, the DC component E of the received signal... r0 The DC component E0 added during transmission is different from the DC component E0 added during transmission, so they cannot be directly subtracted. The mean of the real part of the minimum phase signal is taken as the DC component E of the received signal. r0 Value:
[0120]
[0121] Where real(x) represents taking the real part of x, and n is the number of data points.
[0122] The present invention also provides a directly probed Gaussian modulation continuous variable quantum key distribution system. The directly probed Gaussian modulation continuous variable quantum key distribution system can be implemented by executing the process steps of the directly probed Gaussian modulation continuous variable quantum key distribution method. That is, those skilled in the art can understand the directly probed Gaussian modulation continuous variable quantum key distribution method as a preferred embodiment of the directly probed Gaussian modulation continuous variable quantum key distribution system.
[0123] Example 2:
[0124] The present invention also provides a direct-probe Gaussian-modulated continuous-variable quantum key distribution system, the system comprising the following modules:
[0125] Module M1: The transmitter generates two sets of independent Gaussian distributed random numbers, and uses them to generate a Gaussian modulated radio frequency signal. Then, through spectrum shifting and adding a DC component, it is constructed into a minimum phase signal. The signal is used to modulate the light and transmit the optical signal through the optical fiber.
[0126] Module M1.1: The sender generates two sets of independent Gaussian distributed random numbers, loads them onto a raised cosine pulse, and combines the two as the real and imaginary parts respectively to obtain a complex signal;
[0127] Module M1.2: Construct the above complex signal into a minimum phase signal by first shifting the spectrum of the original signal so that the left edge of its frequency band is at 0, and then adding a DC component;
[0128] Module M1.3: After the minimum phase signal is loaded onto the wave, its real and imaginary parts are loaded onto the I and Q channels of the IQ modulator respectively to modulate the light. The modulated optical signal is then transmitted through the optical fiber channel.
[0129] The continuous variable refers to a signal that takes continuously increasing values, as used in the key distribution system.
[0130] The direct detection refers to detecting the intensity information of the optical signal;
[0131] Two sets of Gaussian distributed random numbers are loaded onto a raised cosine pulse to form a complex signal with real and imaginary parts. The signal's spectral width is B, and its spectral range is... arrive
[0132] According to the original signal E s The expression for the minimum phase signal E(t) constructed by (t) is:
[0133] E(t)=E s (t)exp(iπBt)+E0
[0134] Where t represents time, i is the imaginary unit, and the real constant E0 satisfies |E0|>|E s (t)|;
[0135] The signal E′(t) obtained after loading a wave onto the minimum-phase signal E(t) is:
[0136] E′(t)=E(t)exp(i2πf c t)
[0137] Where f c For carrier frequency.
[0138] Module M2: The receiver uses a photodiode to detect the received coherent optical signal and obtain the intensity information of the optical signal;
[0139] The expression for the photocurrent I(t) measured by the photodiode is:
[0140] I(t)=E′(t)| 2 =|E(t)| 2 .
[0141] Module M3: Apply the Kramers-Kronig relation to the obtained light intensity information to obtain its phase information, thereby recovering the original complex signal, and then obtaining the information loaded on the two canonical components. After passing through the reverse negotiation and security enhancement post-processing module, the final security key is generated.
[0142] Module M3.1: Apply the Kramers-Kronig relation to the received photocurrent signal I(t) to obtain the phase information of the minimum phase signal lost during direct detection. The phase information is obtained through Hilbert transform.
[0143] Module M3.2: The amplitude information of the minimum phase signal is obtained directly from the photocurrent signal, and the minimum phase signal can be recovered by combining it with the phase information;
[0144] Module M3.3: Obtain the original and complex signals based on the minimum phase signal. Perform the reverse operation during construction on the minimum phase signal recovered by the receiver to obtain the original and complex signals. First, remove the DC component, and then perform spectrum shifting to move the frequency band center back to the center frequency 0.
[0145] Module M3.4: The receiver extracts data from the recovered complex signal, performs reverse negotiation with the sender, and is a confidentiality enhancement post-processing module to generate the final binary security key;
[0146] Amplitude information A of minimum phase information E (t) is:
[0147]
[0148] Phase information φ recovered by Hilbert transform E (t) is:
[0149]
[0150] Where pv is the Cauchy principal value.
[0151] The minimum phase signal E recovered by the receiver r (t) is:
[0152]
[0153] The receiver uses the minimum phase signal E r (t) yields the original complex signal E rs (t) is:
[0154] E rs (t)=(E r (t)-E r0 )exp(-iπBt);
[0155] Among them, due to the attenuation effect of the channel during transmission, the DC component E of the received signal... r0 The DC component E0 added during transmission is different from the DC component E0 added during transmission, so they cannot be directly subtracted. The mean of the real part of the minimum phase signal is taken as the DC component E of the received signal. r0 Value:
[0156]
[0157] Where real(x) represents taking the real part of x, and n is the number of data points.
[0158] Example 3:
[0159] The main idea of this method is that the sender processes the signal into a minimum phase signal to satisfy the use conditions of the Kramers-Kronig relation (Mecozzi A, Antonelli C, Shtaif M. Kramers–Kronig coherent receiver[J]. Optica, 2016, 3(11): 1220-1227.); the receiver uses a photodiode to directly detect the optical signal to obtain the signal intensity information, and then applies the Kramers-Kronig relation to obtain the phase information, thereby recovering the original complex signal and obtaining the information on the two canonical components. Then, through post-processing steps such as data negotiation and security enhancement, the final security key is generated.
[0160] Figure 1 This invention represents a Gaussian-modulated continuous-variable quantum key distribution structure based on direct detection of the Kramers-Kronig relation. The invention includes the following steps:
[0161] Step A: The sender generates two sets of independent Gaussian distributed random numbers and uses them to generate a Gaussian modulated radio frequency signal. Then, it constructs a minimum phase signal by spectrum shifting and adding a DC component. The radio frequency signal is used to modulate the light and transmit the optical signal through the optical fiber.
[0162] Step B: The receiver uses a photodiode to detect the received coherent optical signal and obtain the intensity information of the optical signal.
[0163] Step C: Apply the Kramers-Kronig relation to the obtained light intensity information to obtain its phase information, thereby recovering the original complex signal, and then obtaining the information loaded on the two canonical components. After post-processing steps such as data negotiation and security enhancement, the final security key is generated.
[0164] Step A includes the following steps:
[0165] Step A1: The sender generates two sets of independent Gaussian distributed random numbers a and b. In this example, the variance of both sets of random numbers is 1. These numbers are applied to a raised cosine pulse, and the two are combined as the real and imaginary parts, respectively, to obtain the complex signal E. s (t), where t represents time, the spectral width is B, and the spectral range is arrive In this example, B = 10MHz. Two sets of Gaussian distributed random numbers are loaded onto a raised cosine pulse as complex signals with real and imaginary parts; their spectral range is... arrive
[0166] Step A2: Construct the minimum phase signal. First, shift the spectrum of the original signal so that the left edge of its frequency band is at 0, then add a DC component E0. The minimum phase signal E(t) is:
[0167] E(t)=E s (t)exp(iπBt)+E0
[0168] Where i is the imaginary unit, and the real constant E0 satisfies |E0|>|E s (t)|.
[0169] Step A3: Apply the minimum phase signal to the wave. The resulting RF signal is:
[0170] E′(t)=E(t)exp(i2πf c t)
[0171] Where f c Let f be the carrier frequency, which is taken as f in this example. c =10MHz. The real and imaginary parts of E′(t) are loaded onto the I and Q channels of the IQ modulator respectively to modulate the light, and the modulated optical signal is transmitted through the optical fiber channel.
[0172] Step B includes the following steps:
[0173] Step B1: The receiver uses a photodiode to directly probe the optical signal received from the fiber optic channel, and the resulting photocurrent I(t) is:
[0174] I(t)=E′(t)| 2 =|E(t)| 2
[0175] Since the photodiode directly detects the amplitude information of the signal, the carrier added in step A3 has no effect on the detection result.
[0176] Step C includes the following steps:
[0177] Step C1: Apply the Kramers-Kronig relation to the received photocurrent signal I(t) to obtain the phase information of the minimum phase signal lost during direct detection. Obtained through the Hilbert transform, the specific expression is:
[0178]
[0179] Where pv represents Cauchy principal value.
[0180] Step C2: The amplitude information of the minimum phase signal can be directly obtained from the photocurrent signal. Combining it with the phase information allows the minimum phase signal to be recovered. Amplitude information A E The expression for (t) is:
[0181]
[0182] The minimum phase signal E recovered by the receiver r (t) is:
[0183]
[0184] Step C3: Obtain the original complex signal from the minimum phase signal. Perform the reverse operation during construction on the minimum phase signal recovered by the receiver to obtain the original complex signal E. rs (t), first remove the DC component, then perform spectrum shifting to move the frequency band center back to the center frequency 0. E rs The expression for (t) is as follows:
[0185] E rs (t)=(E r (t)-E r0 )exp(-iπBt)
[0186] Among them, due to the attenuation effect of the channel during transmission, the DC component E of the received signal... r0 The DC component E0 added during transmission is different from the DC component E0 added during transmission, so they cannot be directly subtracted. The mean of the real part of the minimum phase signal is taken as the DC component E of the received signal. r0 The value of, i.e.:
[0187]
[0188] Where real(x) represents taking the real part of x, and n is the number of data points.
[0189] Step C4: The receiver retrieves the recovered complex signal E rs Data is extracted from (t), and post-processing steps such as data negotiation and confidentiality enhancement are performed with the sender to generate the final binary security key.
[0190] Continuous variables refer to signals that take continuously increasing values, as used in the key distribution system; direct detection refers to detecting the intensity information of the optical signal.
[0191] Those skilled in the art can understand this embodiment as a more specific description of Embodiment 1 and Embodiment 2.
[0192] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.
[0193] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.
Claims
1. A direct-probe Gaussian-modulated continuous-variable quantum key distribution method, characterized in that, The method includes the following steps: Step S1: The sender generates two sets of independent Gaussian distributed random numbers and uses them to generate a Gaussian modulated radio frequency signal. Then, it constructs a minimum phase signal by spectrum shifting and adding a DC component. The signal is used to modulate the light and transmit the optical signal through the optical fiber. Step S2: The receiver uses a photodiode to detect the received coherent optical signal and obtain the intensity information of the optical signal; Step S3: Apply the Kramers-Kronig relation to the obtained light intensity information to obtain its phase information, thereby recovering the original complex signal, and then obtaining the information loaded on the two canonical components. After reverse negotiation and security enhancement post-processing steps, the final security key is generated. Step S3 includes the following steps: Step S3.1: Analyze the received photocurrent signal By applying the Kramers-Kronig relation, the phase information of the minimum phase signal lost during direct detection is obtained, and the phase information is obtained through Hilbert transform; Step S3.2: The amplitude information of the minimum phase signal is obtained directly from the photocurrent signal, and the minimum phase signal can be recovered by combining it with the phase information; Step S3.3: Obtain the original and complex signals based on the minimum phase signal. Perform the reverse operation during construction on the minimum phase signal recovered by the receiver to obtain the original and complex signals. First, remove the DC component, and then perform spectrum shifting to move the frequency band center back to the center frequency 0. Step S3.4: The receiver extracts data from the recovered complex signal, performs reverse negotiation and confidentiality enhancement post-processing steps with the sender, and generates the final binary security key; Amplitude information of minimum phase information for: ； Phase information recovered by Hilbert transform for: ； in Indicates Cauchy's principal value; Minimum phase signal recovered by the receiver for: ； The receiver uses the minimum phase signal Obtain the original signal for: ； Among them, due to the attenuation effect of the channel during transmission, the DC component of the received signal... With the DC component added during transmission They are not the same and cannot be directly subtracted. The mean of the real parts of the minimum phase signals is taken as the DC component of the received signal. Value: ； in Indicates taking The real part, This represents the number of data points.
2. The direct-probe Gaussian modulation continuous-variable quantum key distribution method according to claim 1, characterized in that, Step S1 includes the following steps: Step S1.1: The sender generates two sets of independent Gaussian distributed random numbers, loads them onto a raised cosine pulse, and combines the two as the real and imaginary parts respectively to obtain a complex signal; Step S1.2: Construct the above complex signal into a minimum phase signal by first shifting the spectrum of the original signal so that the left edge of its frequency band is at 0, and then adding a DC component; Step S1.3: After loading the minimum phase signal, the real part and the imaginary part are loaded onto the I and Q paths of the IQ modulator respectively to modulate the light. The modulated optical signal is then transmitted through the optical fiber channel. The continuous variable refers to a signal that takes continuously increasing values, as used in the key distribution system. The direct detection refers to detecting the intensity information of the optical signal; In step S2: the photocurrent measured by the photodiode The expression is: Where t represents time.
3. The direct-probe Gaussian modulation continuous-variable quantum key distribution method according to claim 2, characterized in that, In step S1.1: two sets of Gaussian distributed random numbers are loaded onto a raised cosine pulse as complex signals with real and imaginary parts, the spectral width being B and the spectral range being [missing information]. arrive ; In step S1.2: based on the original signal... Constructed minimum phase signal The expression is: Where i is the imaginary unit and a real constant. satisfy ; In step S1.3: for the minimum phase signal Signal obtained after loading wave for: in For carrier frequency.
4. A direct-probe Gaussian-modulated continuous-variable quantum key distribution system, characterized in that, The system includes the following modules: Module M1: The transmitter generates two sets of independent Gaussian distributed random numbers, and uses them to generate a Gaussian modulated radio frequency signal. Then, through spectrum shifting and adding a DC component, it is constructed into a minimum phase signal. The signal is used to modulate the light and transmit the optical signal through the optical fiber. Module M2: The receiver uses a photodiode to detect the received coherent optical signal and obtain the intensity information of the optical signal; Module M3: Apply the Kramers-Kronig relation to the obtained light intensity information to obtain its phase information, thereby recovering the original complex signal, and then obtaining the information loaded on the two canonical components. After passing through the reverse negotiation and security enhancement post-processing module, the final security key is generated. Module M3 includes the following modules: Module M3.1: Receives the photocurrent signal By applying the Kramers-Kronig relation, the phase information of the minimum phase signal lost during direct detection is obtained, and the phase information is obtained through Hilbert transform; Module M3.2: The amplitude information of the minimum phase signal is obtained directly from the photocurrent signal, and the minimum phase signal can be recovered by combining it with the phase information; Module M3.3: Obtain the original and complex signals based on the minimum phase signal. Perform the reverse operation during construction on the minimum phase signal recovered by the receiver to obtain the original and complex signals. First, remove the DC component, and then perform spectrum shifting to move the frequency band center back to the center frequency 0. Module M3.4: The receiver extracts data from the recovered complex signal, performs reverse negotiation with the sender, and is a confidentiality enhancement post-processing module to generate the final binary security key; Amplitude information of minimum phase information for: ； Phase information recovered by Hilbert transform for: ； in Cauchy principal value; Minimum phase signal recovered by the receiver for: ； The receiver uses the minimum phase signal Obtain the original signal for: ； Among them, due to the attenuation effect of the channel during transmission, the DC component of the received signal... With the DC component added during transmission They are not the same and cannot be directly subtracted. The mean of the real parts of the minimum phase signals is taken as the DC component of the received signal. Value: ； in Indicates taking The real part, This represents the number of data points.
5. The direct-probe Gaussian modulation continuous-variable quantum key distribution system according to claim 4, characterized in that, Module M1 includes the following modules: Module M1.1: The sender generates two sets of independent Gaussian distributed random numbers, loads them onto a raised cosine pulse, and combines the two as the real and imaginary parts respectively to obtain a complex signal; Module M1.2: Construct the above complex signal into a minimum phase signal by first shifting the spectrum of the original signal so that the left edge of its frequency band is at 0, and then adding a DC component; Module M1.3: After the minimum phase signal is loaded onto the wave, its real and imaginary parts are loaded onto the I and Q channels of the IQ modulator respectively to modulate the light. The modulated optical signal is then transmitted through the optical fiber channel. The continuous variable refers to a signal that takes continuously increasing values, as used in the key distribution system. The direct detection refers to detecting the intensity information of the optical signal; In module M2: the photocurrent measured by the photodiode The expression is: Where t represents time.
6. The direct-probe Gaussian modulation continuous-variable quantum key distribution system according to claim 5, characterized in that, In module M1.1: two sets of Gaussian distributed random numbers are loaded onto a raised cosine pulse as complex signals with real and imaginary parts, respectively. The spectral width is B, and the spectral range is... arrive ; In module M1.2: based on the original and complex signals Constructed minimum phase signal The expression is: Where i is the imaginary unit and a real constant. satisfy ; In module M1.3: for the minimum phase signal Signal obtained after loading wave for: in For carrier frequency.