Achievable Precision Research Articles

Decentralized Scheduling for Cooperative Localization With Deep Reinforcement Learning

Cooperative localization is a promising solution to the vehicular high-accuracy localization problem. Despite its high potential, exhaustive measurement and information exchange between all adjacent vehicles are expensive and impractical for applications with limited resources. Greedy policies or hand-engineering heuristics may not be able to meet the requirement of complicated use cases. In this paper, we formulate a scheduling problem to improve the localization accuracy (measured through the Cramer-Rao lower bound) of every vehicle up to a given threshold using the minimum number of measurements. The problem is cast as a partially observable Markov decision process and solved using decentralized scheduling algorithms with deep reinforcement learning, which allow vehicles to optimize the scheduling (i.e., the instants to execute measurement and information exchange with each adjacent vehicle) in a distributed manner without a central controlling unit. Simulation results show that the proposed algorithms have a significant advantage over random and greedy policies in terms of both required numbers of measurements to localize all nodes and achievable localization precision with limited numbers of measurements.

Bounding the average gate fidelity of composite channels using the unitarity

There is currently a significant need for robust and efficient methods for characterizing quantum devices. While there has been significant progress in this direction, there remains a crucial need to precisely determine the strength and type of errors on individual gate operations, in order to assess and improve control as well as reliably bound the total error in a quantum circuit given some partial information about the errors on the components. In this work, we first provide an optimal bound on the total fidelity of a circuit in terms of component fidelities, which can be efficiently experimentally estimated via randomized benchmarking (RB). We then derive a tighter bound that applies under additional information about the coherence of the error, namely, the unitarity, which can also be estimated via a related experimental protocol. This improved bound smoothly interpolates between the worst-case quadratic and best-case linear scaling for composite error channels. As an application we show how our analysis substantially improves the achievable precision on estimates of the infidelities of individual gates under interleaved RB, enabling greater precision for current experimental methods to assess and tune-up control over quantum gate operations.

The walker speaks its graph: global and nearly-local probing of the tunnelling amplitude in continuous-time quantum walks

We address continuous-time quantum walks on graphs, and discuss whether and how quantum-limited measurements on the walker may extract information on the tunnelling amplitude between the nodes of the graphs. For a few remarkable families of graphs, we evaluate the ultimate quantum bound to precision, i.e. we compute the quantum Fisher information (QFI), and assess the performances of incomplete measurements, i.e. measurements performed on a subset of the graph’s nodes. We also optimize the QFI over the initial preparation of the walker and find the optimal measurement achieving the ultimate precision in each case. As the topology of the graph is changed, a non-trivial interplay between the connectivity and the achievable precision is uncovered.

Fundamental noisy multiparameter quantum bounds

Quantum multiparameter estimation involves estimating multiple parameters simultaneously and can be more precise than estimating them individually. Our interest here is to determine fundamental quantum limits to the achievable multiparameter estimation precision in the presence of noise. We first present a lower bound to the estimation error covariance for a noisy initial probe state evolving through a noiseless quantum channel. We then present a lower bound to the estimation error covariance in the most general form for a noisy initial probe state evolving through a noisy quantum channel. We show conditions and accordingly measurements to attain these estimation precision limits for noisy systems. We see that the Heisenberg precision scaling of 1/N can be achieved with a probe comprising N particles even in the presence of noise. In fact, some noise in the initial probe state or the quantum channel can serve as a feature rather than a bug, since the estimation precision scaling achievable in the presence of noise in the initial state or the channel in some situations is impossible in the absence of noise in the initial state or the channel. However, a lot of noise harms the quantum advantage achievable with N parallel resources, and allows for a best precision scaling of {bf{1}}/sqrt{{boldsymbol{N}}}. Moreover, the Heisenberg precision limit can be beaten with noise in the channel, and we present a super-Heisenberg precision limit with scaling of 1/N2 for optimal amount of noise in the channel, characterized by one-particle evolution operators. Furthermore, using γ-particle evolution operators for the noisy channel, where γ > 1, the best precision scaling attainable is 1/N2γ, which is otherwise known to be only possible using 2γ-particle evolution operators for a noiseless channel.

The positronium hyperfine structure: Progress towards a direct measurement of the 23S1 → 21S0 transition in vacuum

We present the current status for the direct measurement of the positronium hyperfine structure using the 23S1 → 21S0 transition. This experiment, currently being commissioned at the slow positron beam facility at ETH Zurich, will be the first measurement of this transition and the first positronium hyperfine splitting experiment conducted in vacuum altogether. This experiment will be free of systematic effects found in earlier experiments, namely the inhomogeneity in static magnetic fields and the extrapolation from dense gases to vacuum. The achievable precision is expected to be on the order of 10 ppm while the systematic uncertainty is estimated to be within a few ppm. This would allow to check recent bound state QED calculations and a 3σ discrepancy with earlier experiments.

Ancilla-induced amplification of quantum Fisher information

Given a quantum state with an unknown parameter, the Quantum Fisher Information (QFI) is a measure of the amount of information that an observable can extract about the parameter. QFI also quantifies the maximum achievable precision in estimating the parameter with a given amount of resource via an inequality known as quantum Cramer-Rao bound. In this work, we describe a protocol to amplify QFI of a single target qubit precorrelated with a set of ancillary qubits. A single quadrature measurement of only ancillary qubits suffices to perform the complete quantum state tomography (QST) of the target qubit. We experimentally demonstrate this protocol using an NMR system consisting of a $^{13}$C nuclear spin as the target qubit and three $^1$H nuclear spins as ancillary qubits. We prepare the target qubit in various initial states, perform QST, and estimate the amplification of QFI in each case. We also show that the QFI-amplification scales linearly with the number of ancillary qubits and quadratically with their purity.

Estimation of general Hamiltonian parameters via controlled energy measurements

The quantum Cram\'er-Rao theorem states that the quantum Fisher information (QFI) bounds the best achievable precision in the estimation of a quantum parameter $\xi$. This is true, however, under the assumption that the measurement employed to extract information on $\xi$ are regular, i.e. neither its sample space nor its positive-operator valued elements depend on the (true) value of the parameter. A better performance may be achieved by relaxing this assumption. In the case of a general Hamiltonian parameter, i.e. when the parameter enters the system's Hamiltonian in a non-linear way (making the energy eigenstates and eigenvalues $\xi$-dependent), a family of non-regular measurements, referred to as controlled energy measurements, is naturally available. We perform an analytic optimization of their performance, which enables us to compare the optimal controlled energy measurement with the optimal Braunstein-Caves measurement based on the symmetric logarithmic derivative. As the former may outperform the latter, the ultimate quantum bounds for general Hamiltonian parameters are different than those for phase (shift) parameters. We also discuss in detail a realistic implementation of controlled energy measurements based on the quantum phase estimation algorithm and work out a variety of examples to illustrate our results.

Universal Quantum Magnetometry with Spin States at Equilibrium.

We address metrological protocols for the estimation of the intensity and the orientation of a magnetic field, and show that quantum-enhanced precision may be achieved by probing the field with an arbitrary spin at thermal equilibrium. A general expression is derived for the ultimate achievable precision, as given by the quantum Fisher information. The optimal observable is shown to correspond to the spin projection along a temperature-dependent direction, and allows a maximally precise parameter estimation also through ensemble measurements. Finally, we prove the robustness of our scheme against deviations of the measured spin projection from optimality.

Quantum-optical tests of Planck-scale physics

Recently it was proposed to use cavity-optomechanical systems to test for quantum gravity corrections to quantum canonical commutation relations [Nat. Phys. 8, 393-397 (2012)]. Improving the achievable precision of such devices represents a major challenge that we address with our present work. More specifically, we develop sophisticated paths in phase-space of such optomechanical system to obtain significantly improved accuracy and precision under contributions from higher-order corrections to the optomechanical Hamiltonian. An accurate estimate of the required number of experimental runs is presented based on a rigorous error analysis that accounts for mean photon number uncertainty, which can arise from classical fluctuations or from quantum shot noise in measurement. Furthermore, we propose a method to increase precision by using squeezed states of light. Finally, we demonstrate the robustness of our scheme to experimental imperfection, thereby improving the prospects of carrying out tests of quantum gravity with near-future optomechanical technology.

A systematic approach to determining the properties of an iodine absorption cell for high-precision radial velocity measurements

Absorption cells filled with diatomic iodine are frequently employed as wavelength reference for high-precision stellar radial velocity determination due their long-term stability and low cost. Despite their wide-spread usage in the community, there is little documentation on how to determine the ideal operating temperature of an individual cell. We have developed a new approach to measuring the effective molecular temperature inside a gas absorption cell and searching for effects detrimental to a high precision wavelength reference, utilizing the Boltzmann distribution of relative line depths within absorption bands of single vibrational transitions. With a high resolution Fourier transform spectrometer, we took a series of 632 spectra at temperatures between 23{\deg}C and 66{\deg}C. These spectra provide a sufficient basis to test the algorithm and demonstrate the stability and repeatability of the temperature determination via molecular lines on a single iodine absorption cell. The achievable radial velocity precision is found to be independent of the cell temperature and a detailed analysis shows a wavelength dependency, which originates in the resolving power of the spectrometer in use and the signal-to-noise ratio. Two effects were found to cause apparent absolute shifts in radial velocity, a temperature-induced shift of the order of 1 m/s/K and a more significant effect resulting in abrupt jumps of 50 m/s is determined to be caused by the temperature crossing the dew point of the molecular iodine.

Revealing Compartmentalized Diffusion in Living Cells with Interferometric Scattering Microscopy

The spatiotemporal organization and dynamics of the plasma membrane and its constituents are central to cellular function. Fluorescence-based single-particle tracking has emerged as a powerful approach for studying the single molecule behavior of plasma-membrane-associated events because of its excellent background suppression, at the expense of imaging speed and observation time. Here, we show that interferometric scattering microscopy combined with 40 nm gold nanoparticle labeling can be used to follow the motion of membrane proteins in the plasma membrane of live cultured mammalian cell lines and hippocampal neurons with up to 3 nm precision and 25 μs temporal resolution. The achievable spatiotemporal precision enabled us to reveal signatures of compartmentalization in neurons likely caused by the actin cytoskeleton.

Beating the classical precision limit with spin-1 Dicke states of more than 10,000 atoms

Interferometry is a paradigm for most precision measurements. Using N uncorrelated particles, the achievable precision for a two-mode (two-path) interferometer is bounded by the standard quantum limit (SQL), [Formula: see text], due to the discrete (quanta) nature of individual measurements. Despite being a challenging benchmark, the two-mode SQL has been approached in a number of systems, including the Laser Interferometer Gravitational-Wave Observatory and today's best atomic clocks. For multimode interferometry, the SQL becomes [Formula: see text] using M modes. Higher precision can also be achieved using entangled particles such that quantum noises from individual particles cancel out. In this work, we demonstrate an interferometric precision of [Formula: see text] dB beyond the three-mode SQL, using balanced spin-1 (three-mode) Dicke states containing thousands of entangled atoms. The input quantum states are deterministically generated by controlled quantum phase transition and exhibit close to ideal quality. Our work shines light on the pursuit of quantum metrology beyond SQL.

Fundamental limits to frequency estimation: a comprehensive microscopic perspective

We consider a metrology scenario in which qubit-like probes are used to sense an external field that affects their energy splitting in a linear fashion. Following the frequency estimation approach in which one optimizes the state and sensing time of the probes to maximize the sensitivity, we provide a systematic study of the attainable precision under the impact of noise originating from independent bosonic baths. Specifically, we invoke an explicit microscopic derivation of the probe dynamics using the spin-boson model with weak coupling of arbitrary geometry. We clarify how the secular approximation leads to a phase-covariant (PC) dynamics, where the noise terms commute with the field Hamiltonian, while the inclusion of non-secular contributions breaks the PC. Moreover, unless one restricts to a particular (i.e., Ohmic) spectral density of the bath modes, the noise terms may contain relevant information about the frequency to be estimated. Thus, by considering general evolutions of a single probe, we study regimes in which these two effects have a non-negligible impact on the achievable precision. We then consider baths of Ohmic spectral density yet fully accounting for the lack of PC, in order to characterize the ultimate attainable scaling of precision when N probes are used in parallel. Crucially, we show that beyond the semigroup (Lindbladian) regime the Zeno limit imposing the 1/N3/2 scaling of the mean squared error, recently derived assuming PC, generalises to any dynamics of the probes, unless the latter are coupled to the baths in the direction perfectly transversal to the frequency encoding—when a novel scaling of 1/N7/4 arises. As our microscopic approach covers all classes of dissipative dynamics, from semigroup to non-Markovian ones (each of them potentially non-phase-covariant), it provides an exhaustive picture, in which all the different asymptotic scalings of precision naturally emerge.

The mass and age of the first SONG target: the red giant 46 LMi

Context.The Stellar Observation Network Group (SONG) is an initiative to build a worldwide network of 1m telescopes with high-precision radial-velocity spectrographs. Here we analyse the first radial-velocity time series of a red-giant star measured by the SONG telescope at Tenerife. The asteroseismic results demonstrate a major increase in the achievable precision of the parameters for red-giant stars obtainable from ground-based observations. Reliable tests of the validity of these results are needed, however, before the accuracy of the parameters can be trusted.Aims.We analyse the first SONG time series for the star 46 LMi, which has a precise parallax and an angular diameter measured from interferometry, and therefore a good determination of the stellar radius. We use asteroseismic scaling relations to obtain an accurate mass, and modelling to determine the age.Methods.A 55-day time series of high-resolution, high S/N spectra were obtained with the first SONG telescope. We derive the asteroseismic parameters by analysing the power spectrum. To give a best guess on the large separation of modes in the power spectrum, we have applied a new method which uses the scaling of Kepler red-giant stars to 46 LMi.Results.Several methods have been applied: classical estimates, seismic methods using the observed time series, and model calculations to derive the fundamental parameters of 46 LMi. Parameters determined using the different methods are consistent within the uncertainties. We find the following values for the massM(scaling), radiusR(classical), age (modelling), and surface gravity (combining mass and radius):M= 1.09 ± 0.04M⊙,R= 7.95 ± 0.11R⊙aget= 8.2 ± 1.9 Gy, and logg= 2.674 ± 0.013.Conclusions.The exciting possibilities for ground-based asteroseismology of solar-like oscillations with a fully robotic network have been illustrated with the results obtained from just a single site of the SONG network. The window function is still a severe problem which will be solved when there are more nodes in the network.

Characteristics of the Ground-Based User Equipment of Satellite Radio Navigation System Employing Pseudolites in Noisy Environments

This article discusses the joint functioning of satellite radio navigation systems and their augmentations in the form of pseudolite networks under radio interference of various natures and intensities. The achievable precision in determining the coordinates of the object in noisy environments using and considering the estimates of the signal power level of navigational satellites, pseudolites and interference, is an indicator of the effectiveness of such joint systems. The paper refines the model of undisturbed motion of navigation satellites in terms of determining the geocentric coordinates of pseudolites (PL). A model for determining the signal levels of navigation satellites and pseudolites at the input of user equipment (UE) of satellite radio navigation systems (SRNS) was constructed. The algorithm was refined for calculating the mean square error (MSE) to determine coordinates when sharing signals of pseudolites and navigational satellites (NS) in noisy environments. The method was developed and the energy and precision characteristics of SRNS UE operated by NS and PL signals in noisy environments were determined.

The Gaia-ESO Survey: evidence of atomic diffusion in M67?

Investigating the chemical homogeneity of stars born from the same molecular cloud at virtually the same time is very important for our understanding of the chemical enrichment of the interstellar medium and with it the chemical evolution of the Galaxy. One major cause of inhomogeneities in the abundances of open clusters is stellar evolution of the cluster members. In this work, we investigate variations in the surface chemical composition of member stars of the old open cluster M67 as a possible consequence of atomic diffusion effects taking place during the main-sequence phase. The abundances used are obtained from high-resolution UVES/FLAMES spectra within the framework of the Gaia-ESO Survey. We find that the surface abundances of stars on the main sequence decrease with increasing mass reaching a minimum at the turn-off. After deepening of the convective envelope in sub-giant branch stars, the initial surface abundances are restored. We found the measured abundances to be consistent with the predictions of stellar evolutionary models for a cluster with the age and metallicity of M67. Our findings indicate that atomic diffusion poses a non-negligible constraint on the achievable precision of chemical tagging methods.

Strategies for Constraining the Atmospheres of Temperate Terrestrial Planets with JWST

Abstract The Transiting Exoplanet Survey Satellite (TESS) is expected to discover dozens of temperate terrestrial planets orbiting M-dwarfs with atmospheres that could be followed up with the James Webb Space Telescope (JWST). Currently, the TRAPPIST-1 system serves as a benchmark for determining the feasibility and resources required to yield atmospheric constraints. We assess these questions and leverage an information content analysis to determine observing strategies for yielding high-precision spectroscopy in transmission and emission. Our goal is to guide observing strategies of temperate terrestrial planets in preparation for the early JWST cycles. First, we explore JWST’s current capabilities and expected spectral precision for targets near the saturation limits of specific modes. In doing so, we highlight the enhanced capabilities of high-efficiency readout patterns that are being considered for implementation in Cycle 2. We propose a partial saturation strategy to increase the achievable precision of JWST's NIRSpec Prism. We show that JWST has the potential to detect the dominant absorbing gas in the atmospheres of temperate terrestrial planets by the 10th transit using transmission spectroscopy techniques in the near-infrared (NIR). We also show that stacking ⪆10 transmission spectroscopy observations is unlikely to yield significant improvements in determining atmospheric composition. For emission spectroscopy, we show that the MIRI Low Resolution Spectroscopy (LRS) is unlikely to provide robust constraints on the atmospheric composition of temperate terrestrial planets. Higher-precision emission spectroscopy at wavelengths longward of those accessible to MIRI LRS, as proposed in the Origins Space Telescope concept, could help improve the constraints on molecular abundances of temperate terrestrial planets orbiting M-dwarfs.

The New Gas Ion Source at CEDAD: Improved Performances and First 14C Environmental Applications

AbstractA new sputtering ion source has been installed at CEDAD (Centre for Dating and Diagnostics) at the University of Salento in Lecce, Italy. The installation of the new ion source, capable of accepting both solid and gas samples, required significant modifications of the existing low energy injector of the accelerator mass spectrometry (AMS) system. The new ion source is connected, through an in-house designed gas handling interface, to an elemental analyzer which combusts the samples to carbon dioxide and splits the gas into an IRMS system and also to the gas feed line of the ion source. This arrangement allows the simultaneous measurement of C, N content (in the EA), carbon and nitrogen stable isotopic ratios by IRMS and radiocarbon (14C) by AMS on samples with masses in the microgram range. The results of different tests performed to find optimal operational conditions and to improve the system performances are presented. The performances of the system as a function of the diameter of the glass capillary used to feed the source and the pressure of the gas mixture in the syringe are also presented. The achievable precision and blank levels are discussed together with the results obtained in environmental studies.

A Padé-Weierstrass technique for the rigorous enforcement of control limits in power flow studies

A new technique is presented for solving the problem of enforcing control limits in power flow studies. As an added benefit, it greatly increases the achievable precision at nose points. The method is exemplified for the case of Mvar limits in generators regulating voltage on both local and remote buses. Based on the framework of the Holomorphic Embedding Loadflow Method (HELM), it provides a rigorous solution to this fundamental problem by framing it in terms of optimization. A novel Lagrangian formulation of power-flow, which is exact for lossless networks, leads to a natural physics-based minimization criterion that yields what is plausibly the best solution. For networks with small losses, as is the case in transmission, the ac power flow problem cannot be framed exactly in terms of optimization, but the method still retains its ability to select a solution. This foundation then provides a way to design a HELM scheme to solve for the minimizing solution. Although the use of barrier functions evokes interior point optimization, this method, like HELM, is based on the analytic continuation of a germ (of a particular branch) of the algebraic curve representing the solutions of the system. In this case, since the inequality constraints result in an unavoidable singularity at s=1, direct analytic continuation by means of standard Padé approximation exhibits numerical instabilities. This has been overcome by means of a new analytic continuation procedure, denominated Padé-Weierstrass, that exploits the covariant nature of the power flow equations under certain changes of variables. A side benefit of this procedure is that it can also be used when limits are not being enforced, in order to increase the achievable numerical precision in highly stressed cases.

Accurate computation of gravitational field of a tesseroid

We developed an accurate method to compute the gravitational field of a tesseroid. The method numerically integrates a surface integral representation of the gravitational potential of the tesseroid by conditionally splitting its line integration intervals and by using the double exponential quadrature rule. Then, it evaluates the gravitational acceleration vector and the gravity gradient tensor by numerically differentiating the numerically integrated potential. The numerical differentiation is conducted by appropriately switching the central and the single-sided second-order difference formulas with a suitable choice of the test argument displacement. If necessary, the new method is extended to the case of a general tesseroid with the variable density profile, the variable surface height functions, and/or the variable intervals in longitude or in latitude. The new method is capable of computing the gravitational field of the tesseroid independently on the location of the evaluation point, namely whether outside, near the surface of, on the surface of, or inside the tesseroid. The achievable precision is 14–15 digits for the potential, 9–11 digits for the acceleration vector, and 6–8 digits for the gradient tensor in the double precision environment. The correct digits are roughly doubled if employing the quadruple precision computation. The new method provides a reliable procedure to compute the topographic gravitational field, especially that near, on, and below the surface. Also, it could potentially serve as a sure reference to complement and elaborate the existing approaches using the Gauss–Legendre quadrature or other standard methods of numerical integration.