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.
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.
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.
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 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.
In the field of quantum information science, the development of quantum resources for generating copious entangled photons remains a critical challenge. Leveraging the broad spectral characteristics of the parametric down-conversion process, numerous sideband modes distributed symmetrically around the squeezed light in the frequency domain exhibit quantum noise correlations analogous to einstein-podolsky-rosen (EPR) entanglement, which also termed as sideband entanglement. Owing to their distinct advantages in deterministic entanglement distribution, high-capacity entanglement generation, and high-efficiency detection, continuous-variable entangled sideband modes hold significant promise for applications in quantum information science. In this paper, the development of quantum sideband entanglement and experimental progress over the past two decades are reviewed.
Entangled microwave photons form a fundamental resource for quantum information processing and sensing with continuous variables. We use a low-loss Josephson metamaterial comprising superconducting, non-linear, asymmetric inductive elements to generate frequency-entangled photons from vacuum fluctuations at a rate of 2 giga entangled bits per second spanning over 4 GHz bandwidth. The device is operated as a traveling wave parametric amplifier under Kerr-relieving biasing conditions. Furthermore, we realize the first successfully demonstration of single-mode squeezing in such devices -- 3.1±0.7\,dB below the zero-point level at half of modulation frequency.
Continuous-variable quantum key distribution (CV-QKD) enables the efficient distribution of unconditionally secure keys for both communicating parties. Despite significant advancements in optical-based CV-QKD, a persistent challenge is the limited resilience of optical quantum signals to atmospheric noise in free-space channels. This susceptibility leads to considerable degradation in the performance of optical CV-QKD systems, particularly under adverse climatic conditions. Meanwhile, recent advancements in superconducting quantum computing have driven the demand for quantum communication between spatially separated superconducting processors operating at microwave frequencies. To solve the problems, we propose a Gaussian-modulated coherent-state protocol operating at microwave frequencies, utilizing traveling-wave parametric amplifiers to generate entangled states. Our numerical analysis demonstrates that CV-QKD at microwave frequencies enables secure communication in a free-space channel at room temperature. Furthermore, we show that this protocol outperforms the THz frequency protocol over a distance of 20 m and exhibits stronger immunity to interference. Finally, we consider the impact of microwave antenna gain on the protocol's performance, highlighting the decisive role of antenna gain in determining the maximum transmission distance in practical application scenarios.