The entangled state of continuous variables of microwave frequency is an important resource in the field of quantum. In order to apply it to quantum communication protocol and quantum radar, the entanglement between two spatially separated subsystems, namely dual-path entangled quantum microwave is needed. However, for the circuit that generates the entangled quantum microwave, there is no suitable method to indicate whether the quality of the entangled microwave signal is good or not. Aiming at this problem, we put forward a method of evaluating the quality of dual-path entangled quantum microwave signals generated based on von Neumann entropy. The origin of the entangled quantum microwave is that vacuum state signals are transformed into squeezed state signals in driven pump, so in this paper we use a two-mode squeezed vacuum state to describe the formation of dual-path entangled quantum microwave signal, thus providing the function relation between the photon number and the squeezed parameter. In a communication system, the signal-noise ratio is usually used to express the reliability of system. Entropy is a measure of disorder degree in information. If both of them can be made the analogy, the entropy is used to evaluate the proportion of entangled state signals, the quality of original signals will be evaluated and the relationship among the entropy and squeezed parameter and the photon number will be analyzed. The simulation results show that the photon number in the entangled quantum microwave signal is determined by the squeezed parameter, and there is an index change with the square rule between them. Entropy decreases with the increase of squeezed parameter: its minimum value is 0, and its maximum value can be found from 0.9 to 1. The slope of curve is steep near the maximum, which reflects that the influence of squeezed parameter on the degree of entanglement is obvious, and that the range of optimal value choices in squeezed parameter is very narrow. The optimal value of squeezed parameter is dependent on photon number; it increases with the increase of the photon number. Entropy tends to decrease smoothly with the increase of squeezed parameter and it approximately has a negative exponent relation. The photon number in an actual signal is limited, so the limit value of entropy is estimated to be about 65%. The research shows that the quality of the entangled microwave signal can be improved by choosing appropriate squeezed parameter in different circuits that generate dual-path entangled quantum microwave signals for meeting the actual needs. Therefore, the research can provide the method of choosing the parameters of dual-path entangled quantum microwave circuit and improve the availability of system.
The entangled state of continuous variables of microwave frequency is an important resource in the field of quantum. In order to apply it to quantum communication protocol and quantum radar, the entanglement between two spatially separated subsystems, namely dual-path entangled quantum microwave is needed. However, for the circuit that generates the entangled quantum microwave, there is no suitable method to indicate whether the quality of the entangled microwave signal is good or not. Aiming at this problem, we put forward a method of evaluating the quality of dual-path entangled quantum microwave signals generated based on von Neumann entropy. The origin of the entangled quantum microwave is that vacuum state signals are transformed into squeezed state signals in driven pump, so in this paper we use a two-mode squeezed vacuum state to describe the formation of dual-path entangled quantum microwave signal, thus providing the function relation between the photon number and the squeezed parameter. In a communication system, the signal-noise ratio is usually used to express the reliability of system. Entropy is a measure of disorder degree in information. If both of them can be made the analogy, the entropy is used to evaluate the proportion of entangled state signals, the quality of original signals will be evaluated and the relationship among the entropy and squeezed parameter and the photon number will be analyzed. The simulation results show that the photon number in the entangled quantum microwave signal is determined by the squeezed parameter, and there is an index change with the square rule between them. Entropy decreases with the increase of squeezed parameter: its minimum value is 0, and its maximum value can be found from 0.9 to 1. The slope of curve is steep near the maximum, which reflects that the influence of squeezed parameter on the degree of entanglement is obvious, and that the range of optimal value choices in squeezed parameter is very narrow. The optimal value of squeezed parameter is dependent on photon number; it increases with the increase of the photon number. Entropy tends to decrease smoothly with the increase of squeezed parameter and it approximately has a negative exponent relation. The photon number in an actual signal is limited, so the limit value of entropy is estimated to be about 65%. The research shows that the quality of the entangled microwave signal can be improved by choosing appropriate squeezed parameter in different circuits that generate dual-path entangled quantum microwave signals for meeting the actual needs. Therefore, the research can provide the method of choosing the parameters of dual-path entangled quantum microwave circuit and improve the availability of system.
Entangled microwave signal is the reflection of the quantum characteristics of electromagnetic field in a GHz frequency range. Its generation is mainly dependent on superconducting circuits. Owing to the fact that there is no canonical expression to describe the format of entangled microwave signals, two expressional methods are presented on the basis of analyzing the characteristics of entangled microwave signals. One is in quantum frame, and the other is in classical frame. In quantum frame, we express entangled microwave signals in two-mode squeezed vacuum state. According to input-output relationship and parametric amplifier property in the generating process of entangled microwave signals, we describe the characteristics by two-mode squeezing operator and quantum Langevin equation. In the representation of photon number and Wigner function, we analyze the photon number distribution and the quadrature components' distribution of two-mode squeezed vacuum state, which shows the entangled two-photon correlation and the non-localized positive (negative) correlation of quadrature components. These are consistent with the characteristics of entangled microwave signals. Therefore, the results demonstrate that the entangled microwave signals can be expressed by two-mode squeezed vacuum state. In classical frame, we express entangled microwave signals in correlated random signals approximately. According to the relationship between quadrature components and the quantization of electromagnetic field, we construct the relation among electric-field intensity, input angular frequency, and squeezed parameter. The random number with Gaussian distribution is used as an input state to implement the simulation analysis. We illustrate the waveforms of entangled microwave signals after measurement and the extracted quadrature component waveform varying with time. The simulation results are consistent with the measurement results. These results show that the classical expression can reflect the one-path randomicity and two-path correlativity, which are the intrinsic characteristics of entangled microwave signals. Therefore, it is rational to express entangled microwave signals in correlated random signals. These two expressions properly reflect the continuous variable entanglement characteristics of entangled microwave signals. The expression of two-mode squeezed vacuum state is complete. Plenty of parameters that represent quantum information can be calculated by two-mode squeezed vacuum state, such as entanglement degree or the power of noise fluctuation. The merit of the expression of correlated random signals is intuitive, which makes it easier to understand the nonclassical characteristics of entangled microwave signals.
The generation and detection of dual-path entangled quantum microwave are widely investigated in recent years. Nevertheless, entangled quantum microwave is usually expressed and processed in quantum frame. In order to observe the entangled information and apply it to some fields, we also need to measure it and transform it into the form of electric signals. Therefore, we investigate the time domain waveform of dual-path entangled microwave signals from the view of measurement. In different measurement interval, the waveform of one-path entangled microwave signal is completely random. While the waveforms of two-path entangled microwave signal always meet the relationship of positive correlation or negative correlation. The randomicity and correlativity is the most intrinsic characteristic of entangled microwave signals. By analyzing the relation of mean value, fluctuation, entangled photon number and squeezed parameter, we explain the essence of the quantum stochastic and correlated characteristics in physics. A more intuitive understanding of entangled microwave signals would be felt in this research, which makes us easier to utilize the characteristic for the potential applications.
Quantum entanglement possesses important applications in quantum computation, quantum communication, and quantum precision measurement. It is also an important method to improve the performance of quantum radar and quantum radio navigation. However, the penetration of light wave is poor due to the high frequency, which leads to detecting limitations in bad weather. In this context, quantum entanglement in the microwave domain has been extensively studied, and it is hopeful to overcome the above-mentioned defects in quantum optics. Although the entangled microwave preparation of continuous variable is achievable at present, there exist still some problems such as poor entanglement performance, low entanglement efficiency, complex signal processing and control, which restrict the development of entangled microwave sources. In order to improve the entanglement performance in microwave domain, a squeezing-angle locking scheme based on single photon counting is proposed. First, two Josephson parametric amplifiers (JPAs) are driven respectively by two pump signals to generate two single-mode squeezed states which are uncorrelated to each other. Next, the squeezing angle difference between the two single-mode squeezed states is adjusted to 180°, and then the two signals are mixed in a superconducting 180° hybrid ring coupler for two entangled microwave outputs. The outputs are single photon detected, and the results are sent to the data processor for solution. The squeezing angle difference between the input single-mode squeezed microwaves is estimated by Bayesian criterion and compared with the target value to calculate the error. Finally, the squeezing angle correction information is fed back into the JPA pump to control the squeezing angle of the single-mode squeezed microwave of the JPA output as well as the relative squeezing angle to reach the target value. Thus, the dual-path entangled microwave with the optimal entanglement performance is output. Comparing with the existing entangled microwave preparation schemes, a single photon counter is utilized in the scheme of this paper, which leads to a detection efficiency of 90%. In addition, the Bayesian criterion is used to estimate the output result, and the theoretical precision reaches the quantum Cramer-Rao lower bound. Meanwhile, the introduced noise level and operation difficulty are reduced, which greatly improves the property of dual-path entangled microwave preparation.
A method for evaluating the entanglement efficiency of dual-path entangled microwaves based on second-order correlation detection is proposed in this paper. The relationship between the squeezing degree and the entanglement efficiency in the lossless case was analyzed using the second-order interference visibility as the indicator based on measurements of the signal field strength. A loss model was established to analyze the relationship between the average thermal photons, squeezing degree, and entanglement efficiency in the lossy case. The results show that in the lossless case, a larger squeezing degree leads to a lower percentage of entangled photons, giving a lower entanglement efficiency. The entanglement efficiency first increases and then decreases with the increase of the squeezing degree in the lossy case, where the maximum achievable entanglement efficiency depends on the average thermal photons. The lower number the average thermal photons, the higher the maximum achievable entanglement efficiency, and the lower the corresponding squeezing degree. The research results provide a theoretical reference to balance the entanglement degree and entanglement efficiency of industrially-prepared dual-path entangled microwaves.
In recent years, the great progress of studying the quantum entanglement has been made. In the field of optics, the great success has been achieved in quantum entanglement theory and technology. Then researchers concentrate on the microwave frequency band whose frequency is lower than that of optical frequency band. The signal in the microwave frequency band has a longer wavelength, and it has the diffraction capability that the optical signal does not possess. Furthermore, it can spread further in complex environments. Now it is possible to experimentally produce squeezed state of microwave signals and spatially separated path-entangled microwave signals. It is an important issue to judge whether the microwave signals received through dual paths are in entanglement state. In this paper, we firstly introduce the method of using squeezed state of microwave and microwave beam splitter to prepare path-entangled microwave signals. Then we use entanglement witness method to detect entanglement. Through constructing the entanglement witness operator in path-entangled microwave signals, the entanglement of path-entangled microwave signals can be effectively detected. We decompose the expression of the continuous variables path-entangled microwave signals into a large number of 2 2 entangled superposition states, deduce an entangled witness operator of path-entangled microwave signals based on the principle of partial transpose criterion and entanglement witnessing, and prove that the entangled witness can be used to detect the path-entangled microwave signals. Finally, we propose a physical verification of path-entangled microwave signal entanglement. The verification can be realized as follows:firstly, we reverse the phase of a received quantum-state microwave signal by utilizing continuous variable controlled phase gate in a range of 0-, then we send two microwave signals into the two input ports of the microwave beam splitter, and we operate coincidence counting of microwave photons on the two output ports after entanglement microwave signals have passed through the microwave splitter. By analyzing the results of the whole process, we have the following conclusions:if the coincidence rate of two input signals is higher than that of non-entangled microwave signals under the same power, signals can be counted as entanglement. The proposed method can detect the entangled microwave signals more efficiently than the conventional methods, such as quantum state reconstruction, and thus reduce the detection and computational complexity. The entanglement of the two microwave quantum state signals can be observed directly by using this method. This paper provides a new idea for detecting the path-entangled microwave signals.
In this paper, an explicit expression for the maximum detection range of an entangled quantum two-mode squeezed (QTMS) radar, in which a two-mode squeezed vacuum state of microwave electromagnetic fields is used, have been derived by considering both the quantum properties of the entangled microwave fields and radar parameters. By comparing this equation with that of traditional radars, we showed that one can though a QTMS radar as a traditional radar with a reduced threshold signal-to-noise ratio. By discussing the current limitations, it has been shown that the critical parameter to have both simultaneous quantum advantage and substantial radar range is increasing the bandwidth of the generated output signal in the quantum entangled source. It has been shown that by considering the current feasible system parameters, it is possible to implement a QTMS radar with maximum detection range up to the order of 2km, which is suitable for recognizing small unmanned aerial vehicles in urban distances. Moreover, based on the false alarm rate, we introduce two classes of early alarm and track QTMS radars. The present approach can be generalized to other quantum radars with different types of quantum sources like electro-opto-mechanical sources, and also may shed new light on investigating the quantum radar system toward practical applications. Finally, we have discussed the potential outlooks to improve and develop the quantum entangled radar systems to be practical from the engineering point of view.