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.
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.
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.
Abstract Quantum illumination theoretically promises up to a 6 dB error‐exponent advantage in target detection over the best classical protocol. The advantage is maximised by a regime that includes a very high background, which occurs naturally when one considers microwave operation. Such a regime has well‐known practical limitations, though it is clear that, theoretically, knowledge of the associated classical benchmark in the microwave is lacking. The requirement of amplifiers for signal detection necessarily renders the optimal classical protocol here different to that which is traditionally used, and only applicable in the optical domain. This work outlines what is the true classical benchmark for the microwave Quantum illumination using coherent states, providing new bounds on error probability and closed formulae for the receiver operating characteristic, for both optimal (based on quantum relative entropy) and homodyne detection schemes. An alternative source generation procedure based on coherent states is also proposed, which demonstrates the potential to make classically optimal performances achievable in optical applications. The same bounds and measures for the performance of such a source are provided, and its potential utility in the future of room temperature quantum detection schemes in the microwave is discussed.
Based on the characteristics of superposition, entanglement, non-locality and non-clonality of quantum mechanics, quantum information science can break through the physical limits of classical information and open up a new information processing function different from classical electromagnetic application methods. Due to the advantages of high-energy single photon in practical applications, the research and application of optical quantum information technology dominates the development of current quantum information technology. However, the free-space transmission of light waves is greatly affected by weather conditions and atmospheric particles. Comparing with other wave bands, classical microwave signal shows good penetration ability when transmitting in free space. By introducing quantum mechanics, microwave signal also exhibits non-classical merits. As quantum microwave signal inherits both classical transmission performance and quantum non-classical features, it can be utilized as a significant signal source for diverse applications in microwave domain, such as quantum communication, quantum navigation and quantum radar, which are based on quantum technologies in large scale and dynamic free space transmission. There are three main experimental platforms on which quantum microwave is studied and produced. They are cavity quantum electrodynamics(C-QED) system, circuit quantum electrodynamics(c-QED) system, and cavity electro-opto-mechanical(EOM) system, involving with several nonlinear effects such as Kerr effect, Casimir effect, three-wave mixing, etc. In this paper, the setups of these platforms and the preparation principles are introduced. Meanwhile, the preparation principles and methods of microwave single photon, entangled microwave photons, squeezed microwave fields and entangled microwave fields are summarized and analyzed in detail from three aspects. The present status of experimental progress in the relevant fields are summarized and listed as well. Besides, key problems in the application of quantum navigation in free space utilizing quantum microwave are probed. Among them, the most pressing ones are preparation ability, decoherence in transmission and detection of entangled quantum microwave signals, which are also discussed and analyzed in this paper. Finally, we look forward to the future development of quantum microwave technology. It mainly consists of manufacturing microwave detectors with high efficiency, designing thermal photon filters, and developing suitable antennas. We hope that this study can provide useful reference for scholars who are engaged in or interested in research related to quantum microwave technologies.
There are the common problems of limited precision, low anti-interference ability and poor signal detection performance in the classical radio navigation angle measurement systems. To solve these problems, we present a radio navigation angle measurement method realized by entangled microwave signals. Entangled microwave signals are transmitted to free-space and the quadrature components of the signals are measured in the receiving end. When delaying transmitting signals in continuous real time, the correlated baseline generated by the correlation peak of entangled microwave signals will scan back and forth with high-speed. A receiver situated in the scanning areas could measure the contiguous interval of signals. According to the mathematical relation, the azimuth of the receiver relative to centerline could be derived. Imagining applying it to the landing process of aircraft, we design the implementation scheme and devices. With the quantum space-time correlation and no-clone characteristics, there are superior precision, anti-multipath interference ability and signal detection performance for entangled microwave signals. Our research will serve as a new way for radio navigation angle measurement systems.
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.