Quantum Fourier Transform and Phase Estimation in Qudit System

The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case run in a qudit quantum computer, and the quantum circuits are They can be seen as subroutines in a main program given.

Super-sensitive phase estimation with coherent boosted light using parity measurements

We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach-Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer- Rao bound than the pure active （e.g., SU（1, I）） interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [Phys. Rev. D 23 1693 （1981）], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves＇ scheme.

Phase estimation of phase shifts in two arms for an SU(1,1)interferometer with coherent and squeezed vacuum states

We theoretically study the quantum Fisher information（QFI） of the SU（1,1） interferometer with phase shifts in two arms by coherent squeezed vacuum state input, and give the comparison with the result of phase shift only in one arm.Different from the traditional Mach–Zehnder interferometer, the QFI of single-arm case for an SU（1,1） interferometer can be slightly higher or lower than that of two-arm case, which depends on the intensities of the two arms of the interferometer.For coherent squeezed vacuum state input with a fixed mean photon number, the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other.

Enhancing the precision of phase estimation by weak measurement and quantum measurement reversal

The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal quantum Fisher information （QFI） and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.

A Phase Estimation Algorithm for Quantum Speed-Up Multi-Party Computing

Security and privacy issues have attracted the attention of researchers in the field of IoT as the information processing scale grows in sensor networks.Quantum computing,theoretically known as an absolutely secure way to store and transmit information as well as a speed-up way to accelerate local or distributed classical algorithms that are hard to solve with polynomial complexity in computation or communication.In this paper,we focus on the phase estimation method that is crucial to the realization of a general multi-party computing model,which is able to be accelerated by quantum algorithms.A novel multi-party phase estimation algorithm and the related quantum circuit are proposed by using a distributed Oracle operator with iterations.The proved theoretical communication complexity of this algorithm shows it can give the phase estimation before applying multi-party computing efficiently without increasing any additional complexity.Moreover,a practical problem of multi-party dating investigated shows it can make a successful estimation of the number of solution in advance with zero communication complexity by utilizing its special statistic feature.Sufficient simulations present the correctness,validity and efficiency of the proposed estimation method.

A new maximum-likelihood phase estimation method for X-ray pulsar signals

X-ray pulsar navigation(XPNAV) is an attractive method for autonomous navigation of deep space in the future. Currently, techniques for estimating the phase of X-ray pulsar radiation involve the maximization of the general non-convex object functions based on the average profile from the epoch folding method. This results in the suppression of useful information and highly complex computation. In this paper, a new maximum likelihood(ML) phase estimation method that directly utilizes the measured time of arrivals(TOAs) is presented. The X-ray pulsar radiation will be treated as a cyclo-stationary process and the TOAs of the photons in a period will be redefined as a new process, whose probability distribution function is the normalized standard profile of the pulsar. We demonstrate that the new process is equivalent to the generally used Poisson model. Then, the phase estimation problem is recast as a cyclic shift parameter estimation under the ML estimation, and we also put forward a parallel ML estimation method to improve the ML solution. Numerical simulation results show that the estimator described here presents a higher precision and reduces the computational complexity compared with currently used estimators.

Synthetic aperture sonar movement compensation algorithm based on time-delay and phase estimation

The effects of movement errors on imaging results of synthetic aperture sonar and the necessity of movement compensation are discussed. Based on analyzing so-called displaced phase center algorithm, an improved algorithm is proposed. In this method, the time delay is estimated firstly, then the phase is estimated for the residual error, so that the range of movement error suited to the algorithm is extended to some extent. Some simulation results on computer and experimental results in the test tank using the proposed algorithm are given as well.

Measuring small longitudinal phase shifts via weak measurement amplification

Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted into phase signals,it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement.Here,we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation,which is suitable for polarization interferometry.We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference.Besides,we analyze the effect of magnification error which is never considered in the previous works,and find the constraint on the magnification.Our results may find important applications in high-precision measurements,e.g.,gravitational wave detection.

Blind estimation of phase offset in OFDM subcarrier for coherent demodulation

An adaptive algorithm named low complexity phase off- set estimation （LC-POE） is proposed for orthogonal frequency division multiplexing （OFDM） signals. Depending on the requirement, the estimation procedure is divided into several scales to accelerate the adaptive convergence speed and ensure the estimation accuracy. The true phase offset is estimated through shrinking the detection range and raising the resolution scale step by step. Both the convergence performance and complexity are discussed in the paper. Simulation results show the effectiveness of the proposed algorithm. The LC-POE algorithm is promising in the application of OFDM systems.

IMPROVEMENT OF PHASE GRADIENT AUTOFOCUS ALGORITHM

The phase error estimated by phase gradient autofocus(PGA) is not based on a finite order polynomial mode, so PGA has a good autofocus property for arbitrary order phase error and is fit for high resolution airborne SAR. But PGA has two shortcomings: first, it has a worse estimation property for fast changing phase error; second, there exists a section of linear phase in the phase error estimated by this algorithm. This paper introduces the idea of rank one phase estimate (ROPE) autofocus technique, and improves PGA. The improved PGA(IPGA) can successfully overcome both these shortcomings of PGA.

Enhanced multi-baseline unscented Kalman filtering phase unwrapping algorithm

This paper presents an enhanced multi-baseline phase unwrapping algorithm by combining an unscented Kalman filter with an enhanced joint phase gradient estimator based on the amended matrix pencil model, and an optimal path-following strategy based on phase quality estimate function. The enhanced joint phase gradient estimator can accurately and effectively extract the phase gradient information of wrapped pixels from noisy interferograms, which greatly increases the performances of the proposed method. The optimal path-following strategy ensures that the proposed algorithm simultaneously performs noise suppression and phase unwrapping along the pixels with high-reliance to the pixels with low-reliance. Accordingly, the proposed algorithm can be predicted to obtain better results, with respect to some other algorithms, as will be demonstrated by the results obtained from synthetic data.

Synchronization for the Environment of OFDM Cooperative Communications Based on Preamble Design and Phase Rotation

Timing and carrier frequency offset estimation are critical issue for OFDM cooperative communications. In view of the complexity and high accuracy requirement, 1/2 and 1/4 pilot symbol cycle CAZAC sequence structures are defined as the pilot frequency sequence. Estimation within one symbol cycle is carried out through averaging samples of two neighboring symbol cycles, after which the operation is expanded to all the symbol cycles in one band group. Taking multipath effect into account, the concept of phase rotation is proposed for a further step. Adjust the phase difference of estimated symbols by phase rotation, and cross estimation could be done. Meanwhile, timing scheme works within one cycle training sequence. Theoretical and simulation analysis indicate that CRLB does not only relate to estimation symbol length, but also be influenced by phase difference of estimation symbols seriously. In the condition that the length of estimation is fixed, the bigger the phase rotation angle is, the smaller the CRLB is. The complexity of proposed algorithm is less than full cycle average estimation method for almost 50%. Meanwhile, the estimation accuracy is approximate with the full cycle average estimation method as well. Timing scheme with the defined preamble structure is also proposed. Simulation proves its efficiency.

Design and implementation of code acquisition using sparse Fourier transform

Code acquisition is the kernel operation for signal synchronization in the spread-spectrum receiver.To reduce the computational complexity and latency of code acquisition,this paper proposes an efficient scheme employing sparse Fourier transform(SFT)and the relevant hardware architecture for field programmable gate array(FPGA)and application-specific integrated circuit(ASIC)implementation.Efforts are made at both the algorithmic level and the implementation level to enable merged searching of code phase and Doppler frequency without incurring massive hardware expenditure.Compared with the existing code acquisition approaches,it is shown from theoretical analysis and experimental results that the proposed design can shorten processing latency and reduce hardware complexity without degrading the acquisition probability.

ISAR MOTION COMPENSATION USING ROPE

Motion compensation is a key step for inverse synthetic aperture radar (ISAR) imaging. Many algorithms have been proposed. The rank one phase estimation (ROPE) algorithm is a good estimator for phase error widely used in SAR. The ROPE algorithm is used in ISAR phase compensation and the concrete implementation steps are presented. Subsequently, the performance of ROPE is analyzed. For ISAR data that fit the ROPE algorithm model, an excellent compensation effect can be obtained with high computation efficiency. Finally, ISAR real data are processed with ROPE and its imaging result is compared with that obtained by the modified Doppler centroid tracking (MDCT) method, which is a robust and good estimator in ISAR phase compensation.

Pulse phase and doppler frequency estimation of X-ray pulsars under conditions of spacecraft and binary motion and its application in navigation

The pulse phase and doppler frequency estimation of X-ray pulsars in dynamic situations and its application in navigation is a problem that has not been fully investigated. In this paper, solutions are proposed to solve this problem under conditions of spacecraft and binary motion. A high-precision doppler frequency (velocity) measurement model as well as a phase (range) measurement model is established. The averaged maximum-likelihood estimator is developed for the dynamic pulse phase estimation. The pulse phase tracking technique is used in the doppler frequency determination. The tracking filter is redesigned and compared with the existing algorithms. The comparison verifies the advantage of the filter algorithm presented in this pa- per. Unlike traditional views, it is found that in dynamic situations, shorter observation interval lengths will result in higher-accuracy phase and frequency estimates as the tracking filter outputs. A photon-level integrated numerical simulation is performed. Simulation results testify to the validity of the proposed phase and doppler frequency estimation scheme, and show that incorporation of velocity measurements as well as the range ones into the navigation estimator will improve the navigation steady-state performance.

Improved STAP algorithm based on APES

Space-time adaptive processing（STAP） has been proven to be one of the best techniques capable of detecting weak moving targets in strong clutter environment and has been widely applied in airborne ground moving target indication（GMTI） radar.This paper applies an amplitude and phase estimation（APES） approach to two aspects of the STAP algorithm.Firstly,APES is applied to accurately describe the clutter characteristic in angle-Doppler domain.Then,APES is incorporated into the standard STAP algorithm to improve its performance without increasing transmitting/receiving channel and pulse number.The experimental examples show that the detection performance can be improved by using the APES technique,as well as the high computational complexity can be avoided.

Quantum metrology

The statistical error is ineluctable in any measurement. Quantum techniques, especially with the development of quantum information, can help us squeeze the statistical error and enhance the precision of measurement. In a quantum system, there are some quantum parameters, such as the quantum state, quantum operator, and quantum dimension, which have no classical counterparts. So quantum metrology deals with not only the traditional parameters, but also the quantum parameters. Quantum metrology includes two important parts： measuring the physical parameters with a precision beating the classical physics limit and measuring the quantum parameters precisely. In this review, we will introduce how quantum characters （e.g., squeezed state and quantum entanglement） yield a higher precision, what the research areas are scientists most interesting in, and what the development status of quantum metrology and its perspectives are.

Measurement and analysis of Doppler shift for high-speed rail scenario

Based on the analysis of the impact of Doppler shift to the railway dedicated mobile communication quality under the condition of high-speed mobility,this paper presents a Doppler shift measurement approach based on the phase estimation of frequency correction channel(FCCH) which correctly reflects the time-varying characteristic of the channel with a testing system developed.The Doppler shift data under the high-speed condition is collected,processed,analyzed,and compared with the simulation results.The scientific laws of the Doppler shift distribution of radio channel under high-speed condition are obtained.These data and analysis are essential for the establishment of high-speed railway Doppler power spectrum model and the development of the key technology of antiDoppler shift.

Phase Residual Estimations for PCVs of Spaceborne GPS Receiver Antenna and Their Impacts on Precise Orbit Determination of GRACE Satellites

In-flight phase center systematic errors of global positioning system（GPS） receiver antenna are the main restriction for improving the precision of precise orbit determination using dual-frequency GPS.Residual approach is one of the valid methods for in-flight calibration of GPS receiver antenna phase center variations（PCVs） from ground calibration.In this paper,followed by the correction model of spaceborne GPS receiver antenna phase center,ionosphere-free PCVs can be directly estimated by ionosphere-free carrier phase post-fit residuals of reduced dynamic orbit determination.By the data processing of gravity recovery and climate experiment（GRACE） satellites,the following conclusions are drawn.Firstly,the distributions of ionosphere-free carrier phase post-fit residuals from different periods have the similar systematic characteristics.Secondly,simulations show that the influence of phase residual estimations for ionosphere-free PCVs on orbit determination can reach the centimeter level.Finally,it is shown by in-flight data processing that phase residual estimations of current period could not only be used for the calibration for GPS receiver antenna phase center of foretime and current period,but also be used for the forecast of ionosphere-free PCVs in future period,and the accuracy of orbit determination can be well improved.

Examination of seasonal variation of the equatorial undercurrent termination in the Eastern Pacifi c diagnosed by ECCO2

Seasonal variations of the equatorial undercurrent(EUC) termination in the Eastern Pacific,and their mechanism were examined using the Estimating the Circulation and Climate of the Ocean,PhaseⅡ(ECCO2).The ECCO2 reproduced a weak and shallow eastward EUC east of the Galapagos Islands,with annual mean transport of half of EUC to the west of the Islands.The diagnosis of zonal momentum equation suggests that the zonal advection(nonlinear terms) drives the EUC beyond the Islands rather than the pressure gradient force.The EUC in the Far Eastern Pacific has the large st core velocity in boreal spring and the smallest one in boreal summer,and its volume transport exhibits two maxima in boreal spring and autumn.The seasonal variability of the EUC in the Eastern Pacific is dominated by the Kelvin and Rossby waves excited by the zonal winds anomalies in the central and Eastern Pacific that are associated with the seasonal relaxation or intensification of the trade wind.In the Far Eastern Pacific to the east of 120°W,the eastward propagation Kelvin waves play a dominate role in the seasonal cycle of the EUC,results in a semiannual fluctuation with double peaks in boreal spring and autumn.A construction of water mass budget suggests that approximately 24.1% of the EUC water east of 100°W has upwelled to the mixed layer by0.35 m/d.The estimated upwelling is stronge st during boreal autumn and weake st during boreal winter.It is also found that approximately 42.6% of the EUC turns westward to feed the south equatorial current(SEC),13.2% flows north of the equator,and 20.1% flows south of the equator,mainly contributing to Peru-Chile undercurrent.