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.
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.
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.
Being dependent on the analysis of intrinsic correlated characteristic between the quadrature components of the entangled microwave field and the uncertainty of measurement, the authors present a classical expression model of the entangled quantum microwave after the measurement. This model describes two correlated random processes. The time‐domain characteristic and quantum characteristic of the expression model are discussed, which indicate the random correlated characteristic. Results are in agreement with the generation experiment of the entangled quantum microwave, which proves the rationality. On one hand, the merit of the classical expression is intuitive, which makes it easier to understand the non‐classical characteristics of the entangled quantum microwave. On the other hand, it is more convenient to investigate the performance of free‐space propagation and receiver detection by classical expression.
We discuss the relationship between the photon frequency used to produce a continuous variable entangled microwave signal and the signal frequency used for its measurement. We analyze the bandwidth of the continuous variable entangled microwave signal and characterize quantum fluctuations using a quantum sideband representation. The quantum fluctuations of entangled microwave signal follow a true random distribution that is similar to noise. And entangled information is reflected by quantum fluctuations. We conclude that the frequency of generated photons corresponds to the center frequency obtained after performing a Fourier transform on the measured signal, whereas the bandwidth of entangled microwave signal is infinite. Due to the high precision of the measurement from its ultra-wideband behavior, as well as the security afforded by the true randomness and non-localized quantum correlation, these entangled microwaves show significant advantages and potential application value in various fields.
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.
This thesis presents the experimental achievements of (1) generating entangled-microwave fields propagating on two physically separate transmission lines and (2) verifying the entangled states with efficient measurements. Shared entanglement between two parties is an essential resource for quantum information processing and quantum communication protocols. Experimentally, entangled pairs of electromagnetic fields can be realized by distributing a squeezed vacuum over two separated modes. As a result, entanglement is revealed by the strong cross-correlations between specific quadratures of the two modes. Although it is possible to verify the presence of entanglement with low-efficiency quadrature measurements, higher detection efficiencies are desired for performing protocols that exploit entanglement with high fidelity.\nIn the microwave regime, Josephson parametric amplifiers (JPAs) fulfill the two major tasks mentioned above: JPAs prepare the required squeezed states to generate entanglement and enable us to perform efficient quadrature measurements. Therefore, for the purposes of entanglement generation and verification, ultralow-noise--frequency-tunable JPAs have been developed. Additionally, to increase the efficiency of entanglement generation, we integrate JPAs with two on-chip microwave passive components, a directional coupler and a quadrature hybrid, to form an entangler circuit. The two-mode entangled states are created at the two output modes of the entangler and are measured with a two-channel measurement apparatus where each of the two channels incorporates a JPA as a single-quadrature preamplifier. By employing this measurement scheme, the two measured quadratures of the two output modes can be chosen independently of each other, enabling a full characterization of the two-mode state. To definitively demonstrate the two-mode entanglement, I prove that the measured quadrature variances satisfy the inseparability criterion.