Coherent Summation Research Articles

Mutually unbiased coherence of Bell Diagonal States* *This work is supported by NSFC under No. 11761073.

This study explores the coherence of Bell-diagonal states under two complete sets of mutually unbiased bases (MUBs), focusing on four measures: the l 1 norm, l p norm, Rényi relative α-entropy, and relative entropy. We initially construct a complete set of MUBs in C4 by incorporating two maximally entangled bases unbiased with respect to the autotensor of mutually unbiased bases (AMUBs), subsequently comparing it with the canonical set documented in existing literature. We establish the expressions for Bell-diagonal states under these two complete sets of MUBs and demonstrate that the aggregate of each coherence measure across both sets is equivalent. Additionally, we present the upper bounds for the sums of the l 1 norm, l p norm, and Rényi relative 2-entropy of coherence. Furthermore, we describe the geometric structure associated with the sum of relative entropy coherence, revealing that an increase in the sum of relative entropy of coherence corresponds to an increase in the parameter of the Bell-diagonal states.

Near Field Scatter from a Body of Revolution

Better understanding of electromagnetic wave propagation through vegetation and forest environments can be achieved with the aid of modeling and simulation. Specifically, modeling the coherent summation of electromagnetic waves due to both single scatter and multi-scatter effects. To accurately perform simulations in lower frequency bands, S-band and below, the Body of Revolution (BOR) Method of Moments (MoM) must be extended to calculate the scattered electric and magnetic near-fields from BOR in the presence of a plane wave. The near field interactions specifically occur during the various higher order scattering harmonics, i.e. 2nd order and greater harmonics. Additionally, the method must accurately capture scattered fields in the presence of a non-plane wave incident upon BOR. The focus of this study is modeling lossy dielectric BOR that are characteristic of vegetation and forest environments, e.g., cylinders representing tree branches. Although the formal electric and magnetic field scattering definitions are known, this report presents analytical formulations of near field scattering from BOR for this implementation of BOR-MoM. The scattered-field extensions are validated using the commercial software FEKO©, which simulates electromagnetic-wave scattering in 3D using MoM formulation of scattered fields.

Sound pressure level determination around the transformer using coherent and incoherent analytical summation methods

In this paper, coherent and incoherent analytical summation methods from elementary sound sources on the transformer’s tank are presented. They aim to determine a one-third-octave spectrum of sound pressure levels (SPL) in points around the transformer. Each part of the transformer’s surface is treated as a separate plane source so the analytical calculation can be applied to find SPL in the surroundings. Reflections from the ground are also considered by putting an image of the plane sources on the other side of the reflecting plane and adding its contributions to the total pressure in the desired points. Grid-like vibration measurements of vibration velocity on the tank surfaces are used as input parameters. Vibrations and sound pressure levels are measured to validate the method on the 5 MVA transformer experimental object. The SPL around the transformer in short-circuit (SC) and open-circuit (OC) tests is measured in the semi-anechoic chamber to compare it with theoretical results. By analyzing the results, the coherent calculation with reflection provided the most accurate results. In the SC operating condition, the normalized root mean square error (NRMSE) is 17.2%, and in the OC operating condition, it is 10.9%. The novelty of the presented method is that it considers complicated transformer geometry where each surface is calculated as a separate noise source. It calculates noise at a distance from the elementary vibration sources, considering phase and reflection from the hard ground, and provides detailed noise maps that can be used for noise modeling around the substations.

Bottom‐bounce ray angle subspace detector in the shadow zone of deep water

AbstractPassive source detection is a challenging problem in the shadow zone, where the sound is contributed primarily by bottom‐bounce rays. The conventional beamforming detector (CBFD), which utilises the sound energy from a single direction, suffers potential significant performance degradation in the multipath‐signal scenario. The matched field detector (MFD) offers optimal performance by exploiting full‐wave field characteristics but is limited due to its reliance on prior ocean environmental knowledge. The authors demonstrate that the incident sound on a near‐surface vertical line array in the shadow zone can be approximated as a coherent sum of two plane waves that share a symmetric arrival angle about the horizontal. This leads to the signal subspace depending only on the arrival angle, which the authors call the bottom‐bounce ray angle subspace (BRAS). With generalised likelihood ratio test theory, the authors further derive the BRAS detector (BRASD). It can utilise the full signal energy under the premise of weak environmental knowledge requirements and is generally superior to the CBFD. Simulation results in a typical deep‐water channel under different source‐position and array configuration conditions demonstrate the effectiveness of the BRASD and suggest that it can even offer a performance comparable to that of the MFD under specific conditions.

Beam steering using delays generated from an optical OAM mode shifting recirculating loop

This paper investigates the performance of generated delays from an orbital angular momentum mode shifting recirculating delay loop (OAM-SL) in simulation using Kirchhoff-Fresnel diffraction (KFD) and the delays applicability for RF signal beam steering applications. OAM-SL is a novel structure that has been recently reported to produce multiple delayed signal replicas on independent OAM carriers using a single compact system. The objective of this research is to explore the impact of several limiting factors on the quality of OAM-SL delays for beam steering applications, such as where there is (i) displacement of the OAM mode shifter, (ii) displacement of the center of the OAM mode demultiplexer at the loop output, and (iii) the limited resolution. The methodology includes: (i) simulating the beam propagation using KFD, (ii) producing the output as a coherent summation of the recirculating beams, and (iii) characterizing the SCR by dividing the power of the recirculating beam (ρ) on its OAM mode by the power accumulated from the other recirculating beams. Our findings show that delays generated from a system with lin=−30, lshift=+1, and a resolution of 1024 pixels can steer a 100 MHz signal at a steering angle of 11.5° in a four antenna system with 0.1° error if loop alignment is perfect. Also, for steering the 100 MHz signal in an eight antenna system, we analyze the system assuming the system loss can be compensated, and a similar result of 0.1° error is obtained. Additionally, we report the beam steering performance at 23.6° and 36.8°.

Image analysis and resolution for detection-based synthetic-aperture passive source localization

This paper follows a detection-theoretic approach for using synthetic-aperture measurements, made at multiple moving passive receivers, in order to form an image showing the locations of stationary sources that are radiating unknown electromagnetic or acoustic waves. The paper starts with a physics-based model for the propagating fields, and, following the general approach of McWhorter et al (2023 arXiv:2302.06816, IEEE Open J. Signal Process. 4 437–51), derives a detection statistic that is used for the image formation. This detection statistic is a quadratic function of the data. Each point in the scene is tested as a possible hypothesized location for a source, and the detection statistic is plotted as a function of location. Because this image formation process is nonlinear, the standard linear methods for determining resolution cannot be applied. This paper shows how to analyze the detection image by first writing the noiseless image as a coherent sum of shifted complex ambiguity functions of the source waveform. The paper then develops a technique for calculating image resolution; resolution is found to depend on the sensor-source geometry and also on the properties (bandwidth and temporal duration) of the source waveform. Optimal filtering of the image is given, but a simple example suggests that optimal filtering may have little effect. Analysis is also given for the case in which multiple sources are present.

A scheme to fix multiple solutions in amplitude analyses* *Supported by the National Natural Science Foundation of China (NSFC) (12061141007, 12175005) and by the National Key R&D Program of China (2022YFA1601904)

Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better understanding of the underlying dynamics. In special cases where two spin-1/2 particles and two (pseudo-) scalar particles are present in the process, multiple equivalent solutions are found owing to intrinsic symmetries in the summed probability density function. In this study, the problem of multiple solutions is discussed, and a scheme to overcome this problem is proposed by fixing some free parameters. Toys are generated to validate the strategy. A new approach to align the helicities of initial- and final-state particles in different decay chains is also introduced.

Mitigating Aberration-Induced Noise: A Deep Learning-Based Aberration-to-Aberration Approach.

One of the primary sources of suboptimal image quality in ultrasound imaging is phase aberration. It is caused by spatial changes in sound speed over a heterogeneous medium, which disturbs the transmitted waves and prevents coherent summation of echo signals. Obtaining non-aberrated ground truths in real-world scenarios can be extremely challenging, if not impossible. This challenge hinders the performance of deep learning-based techniques due to the domain shift between simulated and experimental data. Here, for the first time, we propose a deep learning-based method that does not require ground truth to correct the phase aberration problem and, as such, can be directly trained on real data. We train a network wherein both the input and target output are randomly aberrated radio frequency (RF) data. Moreover, we demonstrate that a conventional loss function such as mean square error is inadequate for training such a network to achieve optimal performance. Instead, we propose an adaptive mixed loss function that employs both B-mode and RF data, resulting in more efficient convergence and enhanced performance. Finally, we publicly release our dataset, comprising over 180,000 aberrated single plane-wave images (RF data), wherein phase aberrations are modeled as near-field phase screens. Although not utilized in the proposed method, each aberrated image is paired with its corresponding aberration profile and the non-aberrated version, aiming to mitigate the data scarcity problem in developing deep learning-based techniques for phase aberration correction. Source code and trained model are also available along with the dataset at http://code.sonography.ai/main-aaa.

Experiments on Coherent Summation of Chaotic Radio Pulses in a Wireless Channel

Experiments on Coherent Summation of Chaotic Radio Pulses in a Wireless Channel

Precise Measurement of the e^{+}e^{-}→D_{s}^{*+}D_{s}^{*-} Cross Sections at Center-of-Mass Energies from Threshold to 4.95GeV.

The process e^{+}e^{-}→D_{s}^{*+}D_{s}^{*-} is studied with a semi-inclusive method using data samples at center-of-mass energies from threshold to 4.95GeV collected with the BESIII detector operating at the Beijing Electron Positron Collider. The Born cross sections of the process are measured for the first time with high precision in this energy region. Two resonance structures are observed in the energy-dependent cross sections around 4.2 and 4.4GeV. By fitting the cross sections with a coherent sum of three Breit-Wigner amplitudes and one phase-space amplitude, the two significant structures are assigned masses of (4186.8±8.7±30) and (4414.6±3.4±6.1) MeV/c^{2}, widths of (55±15±53) and (122.5±7.5±8.1) MeV, where the first errors are statistical and the second ones are systematic. The inclusion of a third Breit-Wigner amplitude is necessary to describe a structure around 4.79GeV.

Non-forward radiative corrections to electron-carbon scattering

Radiative corrections to elastic scattering represent an important part of the interpretation of electron-induced nuclear reactions at small energy transfers, where they represent a dominant part of the background. Here we present and validate a new event generator for simulating QED radiative processes in electron-carbon scattering that exactly calculates the coherent sum of the Bethe-Heitler amplitudes for the leading diagrams. We demonstrate that the generator describes the shape of the radiative tail of an elastic peak with a precision better than 10% over the whole energy range of the scattered electrons and can thus be reliably employed in the analyses of electron scattering experiments for more precise extraction of inelastic cross-sections.

Geometric solutions for focusing retroreflectors

Although focusing might normally be an architectural acoustician’s nightmare, combining it with retroreflection is potentially beneficial. Focusing acoustic retroreflectors concentrate early reflected sound onto arbitrarily located sources. Dihedral and trihedral retroreflectors can be made to focus by curving one or more of their faces in either one or two dimensions. The relationship between curvature and focal distance is developed empirically using analytic ray tracing and finite-difference time-domain methods. Dihedra can be made more compact by segmenting the cross-sectional curvature similar to the Fresnel lens. Complexities of fabricating doubly curved surfaces can be overcome by approximating with several flat surfaces and physical examples are constructed from bending sheet-steel. Simplified designs are shown to achieve similar performance to ideally curved focusing retroreflectors. For context, performance is compared to coherent and incoherent summation of a perfectly reflecting spherical surface of equivalent solid angle, as well as an equivalent flat surface. Results show increased speech-weighted retroreflected energy level and concentration of sound in the region surrounding the collocated source-receiver over the upper range of typical human speech (1 kHz–8 kHz octave bands) when compared to non-focusing retroreflectors, and substantial increases in reflected energy level compared to a specular reflection at normal incidence.

Optical channel aggregation based on modulation format conversion by coherent spectral superposition with electro-optic modulators

Spectrally efficient modulation formats become essential for optical network scaling as the demand for routed data streams exceeds the present wavelength-division multiplexing systems’ throughput. However, achieving high spectral efficiency at high data rates requires complex and bandwidth-intensive electronics. In this study, we propose an all-optical aggregation scheme that combines multiple low spectral efficiency optical wavelength channels from an optical frequency comb based transmitter into fewer channels with higher spectral efficiency. Our method utilizes coherent spectral superposition and optical vector summation, eliminating the need for optical nonlinearities and relying on linear signal processing with an electro-optic modulator. By adjusting the phase of the radio frequency signal driving the modulator, we can easily achieve the required optical phase tuning for vector addition in the I-Q plane. Through experimental demonstrations, we show that the proposed approach enables the generation of 10 GBd PAM-4 and 10 GBd quadrature phase shift keying (QPSK) signals by aggregating two 10 GBd binary phase shift keying signals. Similarly, we aggregate two 10 GBd QPSK signals into one 10 GBd quadrature amplitude modulation-16 (QAM-16) signal. The experiments employ both conventional and sinc-shaped Nyquist signals. Our in-line, all-optical aggregation concept significantly enhances operational capacity while reducing complexity. It offers a promising solution for realizing flexible integrated optical transmitters for advanced modulation format signals using lower-quality electronics. Additionally, it aligns with the requirements of future dynamically reconfigurable optical networks that leverage spectral traffic aggregation. Given its reliance on linear signal processing with an electro-optic modulator, the integration of the method into any integrated photonic platform is straightforward.

Science results from sixteen years of MRO SHARAD operations

In operation for >16 years to date, the Mars Reconnaissance Orbiter (MRO) Shallow Radar (SHARAD) sounder has acquired data at its nominal 300–450 m along-track and 3-km cross-track resolution covering >55% of the Martian surface, with nearly 100% overlap in coverage at that scale in the polar regions and in a number of smaller mid-latitude areas. While SHARAD data have opened a new window into understanding the interior structures and properties of Martian ices, volcanics, and sedimentary deposits up to a few kilometers in depth, they have also led to new revelations about the deeper interior and the behavior of the planet's ionosphere. Here we summarize the data collected by SHARAD over this time period, the methods used in the analysis of that data, and the resulting scientific findings. The polar data are especially rich, revealing complex structures that comprise up to several dozen reflecting interfaces that extend to depths of 3 km, which inform the evolution of Martian climate in the late Amazonian period. SHARAD observations of mid-latitude lobate debris aprons and other glacier-like landforms detect strong basal reflections and low dielectric loss, confirming that they are ice-rich debris-covered glaciers. In other mid-latitude terrains, SHARAD data demonstrate the presence of widespread ground ices, likely at lower concentrations. SHARAD signals also probe non-icy materials, mapping out stacked lava flows, probing low-density materials thought to be ash-fall deposits, and occasionally penetrating sedimentary deposits, all of which reveal the structures and interior properties diagnostic of emplacement processes. SHARAD signals are impacted by their passage through the Martian ionosphere, revealing variations in time and space of the total electron content linked with the remanent magnetic field. Advanced techniques developed over the course of the mission, which include subband and super-resolution processing, coherent and incoherent summing, and three-dimensional (3D) radar imaging, are enabling new discoveries and extending the utility of the data. For 3D imaging, a cross-track spacing at the nominal 3-km resolution is more than sufficient to achieve good results, but finer spacing of 0.5 km or less significantly improves the spatially interpolated radar images. Recent electromagnetic modeling and a flight test show that SHARAD's signal-to-noise ratio can be greatly improved with a large (∼120°) roll of the spacecraft to reduce interference with the spacecraft body. Both MRO and SHARAD are in remarkably fine working order, and the teams look forward to many more years in which to pursue improvements in coverage density, temporal variability in the ionosphere, and data quality that promise exciting new discoveries at Mars.

Rogue wave generation using a chaotic semiconductor laser with energy redistribution.

We demonstrate for the first time that optical rogue waves (RWs) can be generated using a chaotic semiconductor laser with energy redistribution. Chaotic dynamics are numerically generated using the rate equation model of an optically injected laser. The chaotic emission is then sent to an energy redistribution module (ERM) that consists of a temporal phase modulation and a dispersive propagation. The process enables a temporal energy redistribution of the chaotic emission waveforms, where coherent summation of consecutive laser pulses leads to random generation of giant intensity pulses. Efficient generation of optical RWs are numerically demonstrated by varying the ERM operating parameters in the entire injection parameter space. The effects of the laser spontaneous emission noise on the generation of RWs are further investigated. The RW generation approach offers a relatively high flexibility and tolerance in the choice of ERM parameters according to the simulation results.

Time-domain Kirchhoff approximation extensions modeling of acoustic camera imagery with multiple scattering

High-frequency acoustic cameras have provided high-resolution sonar images to enable the development of signal processing algorithms, such as 3-D reconstruction, target recognition, and precision navigation. However, the lack of large datasets has hampered the development of such algorithms. In this context, this paper proposes a time-domain Kirchhoff approximation extensions (TDKAX)-based model to generate realistic acoustic camera images, capable of accounting for multiple scattering from arbitrary-shapetargets. The images are formed by a coherent summation of different orders of transient echoes, along with a pipeline of the range conversion, time-varying gain compensation, noise addition, and image rendering. Validating the proposed model using tank experiments of isolated cylindrical concave reflectors, we then present the ray paths based on the coordinates of intersection points. They can help interpret the mechanism of image features in the absence of amplitude information. Results demonstrate that, with the temporal and spatial coherence of different orders of scattering, the proposed model successfully reproduces forward-looking sonar (FLS) images with multiple scattering arcs and coherent speckles.

New microscopic analysis for 15N(d,p)16N neutron transfer reaction at 15 MeV

Inspired by the prevalent [Formula: see text] cluster structure of deuterons, which appears at an excitation energy of 2.225[Formula: see text]MeV, the recently measured angular distributions (ADs) for [Formula: see text]N([Formula: see text],[Formula: see text]N and [Formula: see text]N([Formula: see text],[Formula: see text]N systems at an energy of 15[Formula: see text]MeV X. Y. Li et al., [Phys. Rev. C 106, (2022) 025807] are microscopically analyzed using the continuum discretized coupled channel (CDCC) method. The extracted [Formula: see text] potential, considered as the coherent sum of cluster folding and dynamical polarization potentials, both derived from the CDCC computations, was then employed to investigate the [Formula: see text]N([Formula: see text],[Formula: see text]N neutron transfer reaction leading to the (2−, 0.0[Formula: see text]MeV), (0−, 0.12[Formula: see text]MeV), (3−, 0.298[Formula: see text]MeV), and (1−, 0.397[Formula: see text]MeV) [Formula: see text]N states. Since extracting reliable information on spectroscopic factors (SFs) is highly dependent on the interaction potential, the extracted [Formula: see text] was employed to get such information. The investigation gives evidence for the applicability of the [Formula: see text] in describing the elastic scattering and the neutron transfer ADs data. The extracted SFs for the [Formula: see text]N states under consideration are consistent with those that have been reported before.

Observation of the Y(4230) and evidence for a new vector charmoniumlike state Y(4710) in e+e−→KS0KS0J/ψ

Cross sections for the process $e^{+} e^{-} \to K_{S}^{0} K_{S}^{0} J/\psi$ at center-of-mass energies from $4.128$ to $4.950$ GeV are measured using data samples with a total integrated luminosity of 21.2 fb$^{-1}$ collected by the BESIII detector operating at the BEPCII storage ring. The $Y(4230)$ state is observed in the energy dependence of the $e^{+} e^{-} \to K_{S}^{0} K_{S}^{0} J/\psi$ cross section for the first time with a statistical significance of 26.0$\sigma$. In addition, an enhancement around $4.710$ GeV, called the $Y(4710)$, is seen with a statistical significance of 4.2$\sigma$. There is no clear structure around $4.484$ GeV. Using a fit with a coherent sum of three Breit-Wigner functions, we determine the mass and width of the $Y(4230)$ state to be $4226.9 \pm 6.6 \pm 21.9$ MeV/$c^{2}$ and $71.7 \pm 16.2 \pm 31.4$ MeV, respectively, and the mass and width of the $Y(4710)$ state to be $4704.0 \pm 52.3 \pm 69.5$ MeV/$c^{2}$ and $183.2 \pm 114.0 \pm 90.8$ MeV, respectively, where the first uncertainties are statistical and the second are systematic. In addition, the average Born cross section ratio of $e^{+} e^{-} \to K_{S}^{0} K_{S}^{0} J/\psi$ to $e^{+} e^{-} \to K^{+} K^{-} J/\psi$ is measured to be $0.388_{-0.028}^{+0.035}\pm0.016$, or $0.426_{-0.031}^{+0.038}\pm0.018$ if three-body phase space is considered.

Coherent curvature radiation spectrum by dynamically fluctuating bunches in magnetospheres

ABSTRACT Coherent curvature radiation by charged bunches has been discussed as the radiation mechanism for radio pulsars and fast radio bursts. Important issues for this radiation mechanism include how the bunches form and disperse in the magnetosphere of a pulsar or magnetar. More likely, bunches form and disperse continuously and it remains unclear what the spectral features are for these fluctuating bunches. In this work, we consider that the bunches in a magnetosphere have a formation rate of λB , a lifetime of τB , and a typical Lorentz factor of γ, and analyse the spectral features of coherent curvature radiation by these fluctuating bunches. We find that the emission spectrum by a single fluctuating bunch is suppressed by a factor of ∼(λB τB )2 compared with that of a single persistent bunch, and there is a quasi-white noise in a wider band in the frequency domain. The high-frequency cutoff of the spectrum is at ∼max (ωpeak, 2γ2/τB ), where ωpeak is the peak frequency of curvature radiation. If the observed spectrum is not white-noise-like, the condition of 2γ2λB ≳ min (ωpeak, 2γ2/τB ) would be required. Besides, the radiation by multiple fluctuating bunches along a field line is the incoherent summation of the radiation by single bunches if the bunch separation is longer than the wavelength. Conversely, a coherent summation should be involved. We also discuss the effects of bunch structures and the mechanism of bunch formation and dispersion.

Polarized Proton Structure in the Resonance Region

In view of the precise data available on inclusive polarized electron scattering off polarized proton targets in the nucleon resonance excitation region, we compare these results with the coherent sum of resonant contributions to the polarized structure function g_1 and virtual photon asymmetry A_1. To this goal, we employ the nucleon resonance electroexcitation amplitudes determined for photon virtualities Q^2 < 5.0 GeV^2 from analyses of the CLAS data on exclusive electroproduction off protons in the resonance region. Most of the well established resonances of four star PDG status in the mass range up to 1.75 GeV are included. We find that the resonance-like structures observed in the inclusive g_1 data are related to the resonant contributions in the entire range of photon virtuality Q^2 where the data on g_1 are available. In the range of invariant mass of the final hadron system W > 1.5 GeV, the data on the asymmetry A_1 are well reproduced even when accounting for resonant contributions only, especially for the larger values of Q^2 and energies analysed. This observation offers an interesting hint to quark-hadron duality seen in polarized inclusive electron scattering observables.