Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fisher information”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Mutual information bounded by Fisher information

We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the literature (e.g., the van Trees inequality) that are useful also for cases where the latter ones give trivial bounds. We then generalize them to the quantum case, where they bound the Holevo information in terms of the quantum Fisher information. We illustrate the usefulness of our bounds with a case study in quantum phase estimation. Here, they allow us to adapt to mutual information (useful for global strategies where the prior plays an important role), the known and highly nontrivial bounds for the Fisher information in the presence of noise. The results are also useful in the context of quantum communication, both for continuous and discrete alphabets. Published by the American Physical Society 2025

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Latent-Variable Formulation of the Poisson Canonical Polyadic Tensor Model: Maximum Likelihood Estimation and Fisher Information

We establish parameter inference for the Poisson canonical polyadic (PCP) tensor model through a latent-variable formulation. Our approach exploits the observation that any random PCP tensor can be derived by marginalizing an unobservable random tensor of one dimension larger. The loglikelihood of this larger dimensional tensor, referred to as the “complete” loglikelihood, is comprised of multiple rank one PCP loglikelihoods. Using this methodology, we first derive maximum likelihood estimators for the PCP model and demonstrate that several existing algorithms for fitting non-negative matrix and tensor factorizations are Expectation-Maximization algorithms. Next, we derive the observed and expected Fisher information matrices for the PCP model. The Fisher information provides us crucial insights into the well-posedness of the tensor model, such as the role that tensor rank plays in identifiability and indeterminacy. For the special case of rank one PCP models, we demonstrate that these results are greatly simplified.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quantum fisher information reveals UV-IR mixing in the strange metal

The density-density response in optimally doped Bi 2 Sr 2 CaCu 2 O 8+$x$ has recently been shown to exhibit conformal symmetry. Using, the experimentally inferred conformal dynamic susceptibility, we compute the resultant quantum Fisher information (QFI), a witness to multi-partite entanglement. For a Fermi liquid, we find that the QFI grows quadratically as the temperature increases, consistent then with the phase space available for scattering in the standard theory of metals. By contrast, the QFI in a strange metal increases as a power law at as the temperature decreases, but ultimately extrapolates to a constant at T=0. The constant is of the form, ω$^{2Δ}_g$, where Δ is the conformal dimension and ω g is the UV cutoff which is on the order of the pseudogap. As this constant depends on both UV and IR properties, it illustrates that multipartite entanglement in a strange metal exhibits UV-IR mixing, a benchmark feature of doped Mott insulators as exemplified by dynamical spectral weight transfer. We conclude with a discussion of the implication of our results for low-energy reductions of the Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1989

Simple proof of the concavity of the entropy power with respect to Gaussian noise

A very simple proof of M. H. Costa's result that the entropy power of Xt = X + N (O, tI) is concave in t, is derived as an immediate consequence of an inequality concerning Fisher information. This relationship between Fisher information and entropy is found to be useful for proving the central limit theorem. Thus, one who seeks new entropy inequalities should try first to find new inequalities about Fisher information, or at least to exploit the existing ones in new ways.

Dembo, Amir↗
NASA NTRS1986

An information measure for class discrimination

This article describes a separability measure for class discrimination. This measure is based on the Fisher information measure for estimating the mixing proportion of two classes. The Fisher information measure not only provides a means to assess quantitatively the information content in the features for separating classes, but also gives the lower bound for the variance of any unbiased estimate of the mixing proportion based on observations of the features. Unlike most commonly used separability measures, this measure is not dependent on the form of the probability distribution of the features and does not imply a specific estimation procedure. This is important because the probability distribution function that describes the data for a given class does not have simple analytic forms, such as a Gaussian. Results of applying this measure to compare the information content provided by three Landsat-derived feature vectors for the purpose of separating small grains from other crops are presented.

Shen, S. S.↗
DOE OSTI2025

Generalized geometric speed limits for quantum observables

Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension ≥3, tighten existing bounds—in some cases by an arbitrarily large multiplicative constant. Our theoretical results are supported by illustrative examples and an experimental demonstration using a superconducting qutrit. We also derive two upper bounds on the generalized quantum Fisher information in terms of the condition number of the density matrix. One of these bounds applies only to coherent dynamics and depends also on the variance of the Hamiltonian. The other bound depends also on the so-called Wigner-Yanase skew information. These bounds generalize well-known bounds on the symmetric logarithmic derivative quantum Fisher information and are tighter than the existing bounds for sufficiently mixed states (e.g., for sufficiently high temperature thermal states).

open quantum systems & decoherence↗
DOE OSTI2025

Optimizing lossy state preparation for quantum sensing using Hamiltonian engineering

One of the most prominent platforms for demonstrating quantum sensing below the standard quantum limit is the spinor Bose–Einstein condensate. While a quantum advantage using several tens of thousands of atoms has been demonstrated in this platform, it faces an important challenge: atom loss. Atom loss is a Markovian error process modeled by Lindblad jump operators, and a no-go theorem, which we also show here, states that the loss of atoms in all spin components reduces the quantum advantage to a constant factor. Here, we show that this no-go theorem can be circumvented if we constrain atom losses to a single spin component. Moreover, we show that in this case, the maximum quantum Fisher information with N atoms scales as N 3/2 , establishing that a scalable quantum advantage can be achieved despite atom loss. Although Lindblad jump operators are generally non-Hermitian and non-invertible, we use their Moore–Penrose inverse to develop a framework for constructing several states with this scaling of Fisher information in the presence of losses. We use Hamiltonian engineering with realistic Hamiltonians to develop experimental protocols for preparing these states. Finally, we discuss possible experimental techniques to constrain the losses to a single spin mode.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1971

Design of optimal probing signals for vector parameter estimation.

In the design of optimal inputs or probing signals for parameter estimation, it is more natural to consider functions of the Fisher information matrix as the criterion of optimality instead of some function of the error covariance matrix. The input which maximizes the Fisher information measure for efficient estimation of a scalar parameter also provides the minimum error variance. The information is thus a logical choice for the optimality criterion in scalar problems. No such obvious choice is apparent for vector parameter estimation. A number of performance measures are examined and compared in the present study, and a useful criterion is selected. The design of an optimal probing signal using this criterion is shown to be equivalent to an optimal control problem in which certain equality constraints must be satisfied. This problem may be solved by conventional techniques of deterministic or stochastic optimal control.

Nahi, N. E.↗
DOE OSTI2025

Identification Uncertainty in Inverse Material Model Parameter Determination: A Sensitivity‐Based Decision Process for Load Path Selection

This research proposes a sensitivity-based framework for selecting the optimal prescribed loading path for a biaxial cruciform specimen. Optimality here is determined by the direction and magnitude of the prescribed displacement that minimizes the influence of random noise on the material model parameter identification. Using simulated experimental data based on finite element simulation, in this work, we identify the material model parameters of a Ludwik hardening model and plane stress implementation of the Hill-48 yield criterion using finite element model updating (FEMU). Our analysis reveals that the identification (or estimator) uncertainty of model parameters depends on the displacement boundary conditions (i.e., loading sequence) and the ground-truth value of the individual parameters. Optimal experimental design (OED) criteria based on the Fisher information matrix were investigated to mitigate indecision in the choice of optimal load path when the identification uncertainty of different material model parameters optimized at different load paths. The determinant of the Fisher information matrix was chosen here as the more useful metric due to its ability to capture uncertainty of the most influential material model parameters. The proposed framework demonstrates potential for real-time automated load step selection using scalar criteria derived prior to mechanical loading. The framework can be generalized to other geometries, boundary conditions and material models, allowing this procedure to be utilized for different experimental configurations and materials.

Fayad, Samuel S. [University of Illinois at Urbana↗
DOE OSTI2024

Detecting Multipartite Entanglement Patterns Using Single-Particle Green’s Functions

Here, we present a protocol for detecting multipartite entanglement in itinerant many-body electronic systems using single-particle Green’s functions. To achieve this, we first establish a connection between the quantum Fisher information and single-particle Green’s functions by constructing a set of witness operators built out of single electron creation and destruction operators in a doubled system. This set of witness operators is indexed by a momentum k. We compute the quantum Fisher information for these witness operators and show that for thermal ensembles it can be expressed as an autoconvolution of the single-particle spectral function. We then apply our framework to a one-dimensional fermionic system to showcase its effectiveness in detecting entanglement in itinerant electron models. We observe that the detected entanglement level is sensitive to the wave vector associated with witness operator. Our protocol will permit detecting entanglement in many-body systems using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, two spectroscopies that measure the single-particle Green’s function. It offers the prospect of the experimental detection of entanglement through spectroscopies beyond the established route of measuring the dynamical spin response.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Modeling and Optimization of a Rotating Packed Bed Contactor with a Tetraamine-Appended Metal−Organic Framework for CO 2 Capture

A potential contactor technology for sorbent-based CO 2 capture is the rotating packed bed that contains separate sections for continuous adsorption and desorption. A heat exchanger can be embedded to remove heat in the adsorption section and add heat in the desorption section. In this work, we develop a two-dimensional (2D) model of a rotating packed bed for use in CO 2 capture applications. Mass and energy balances for the model are developed based on a Ljungström-type air preheater, which accounts for the counter-current axial flow of gas phases in separate sections of the bed and the rotation of a solid sorbent, which cycles between adsorption and desorption sections. The sorbent used for this analysis is the tetraamine-appended metal−organic framework Mg 2 (dobpdc)(3−4− 3), chosen for its stability and affinity for CO 2 at low partial pressures, such as those from a natural gas power plant source. An optimization problem is solved that considers the trade-off between maximizing the productivity of the bed and minimizing energy consumption. Maximum productivity and minimum energy are found to be 8.53 kg/h/m 3 and 3.84 MJ/kg, respectively, when these objectives are optimized independently. It is observed that the flue gas pressure and bed rotational speed are the desired operating variables to vary for model-based design of experiments to reduce uncertainty in parameter estimation, as these two variables yielded the most information content based on the Fisher information matrix.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2026

An information-matching approach to optimal experimental design and active learning

The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict other quantities of interest (QoI). Because models often contain many unidentifiable (sloppy) parameters, QoIs often depend on a relatively small number of parameter combinations. Therefore, we introduce an information-matching criterion based on the Fisher information matrix to select the most informative training data from a candidate pool. This method ensures that the selected data contain sufficient information to learn only those parameters that are needed to constrain downstream QoIs. It is formulated as a convex optimization problem, making it scalable to large models and datasets. Here, we demonstrate the effectiveness of this approach across various modeling problems in diverse scientific fields, including power systems and underwater acoustics. Finally, we use information-matching as a query function within an active learning (AL) loop for materials science applications. In all these applications, we find that a relatively small set of optimal training data can provide the necessary information for achieving precise predictions. These results are encouraging for diverse future applications, particularly AL in large machine-learning models.

Materials science↗
NASA NTRS1977

An information matrix approach for aircraft parameter-insensitive control

The Fisher Information Matrix provides the nucleus of a design procedure for obtaining parameter-insensitive feedback gains in Linear-Quadratic-Gaussian problems. The procedure minimizes a sum of performance and closed-loop sensitivity costs, the latter being related to the information content of the system response. Analytical expressions for the appended cost functional and its gradient with respect to the feedback gains are derived. These derivatives serve as the basis of a computationally efficient iterative algorithm that finds the optimal gains. Application of the technique is made to determine low sensitivity feedback gains for a C-5A wing loading alleviation system that has 15 states and three uncertain parameters.

Kleinman, D. L.↗
DOE OSTI2025

Genuine k -partite correlations and entanglement in the ground state of the Dicke model for interacting qubits

Here, in this work, we calculate and study correlations of the Dicke model in the presence of qubit–qubit interaction. Whereas the analysis of correlations among its subsystems is essential for the understanding of corresponding critical phenomena and for performing quantum information tasks, the majority of correlation measures are restricted to bipartitions due to the inherent challenges associated with handling multiple partitions. To circunvent this we employ the calculation of Genuine Multipartite Correlations (GMC) based on the invariance of our model under particle permutation. We then quantify the correlations within each subpart of the system, as well as the percentage contribution of each GMC of order $k$, highlighting the many-body behaviors for different regimes of parameters. Additionally, we show that GMC signal both first- and second-order quantum phase transitions present in the model. Furthermore, as GMC encompasses both classical and quantum correlations, we employ Quantum Fisher Information (QFI) to detect genuine multipartite entanglement. Ultimately, we map the Dicke model with interacting qubits to spin in solids interacting with a quantum field of magnons, thus demonstrating a potential experimental realization of this model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Estimating time in quantum chaotic systems and black holes

We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation". Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time values. Intuitively, it should become increasingly difficult to estimate the precise value of time by making measurements on the state. We use a quantity called the Fisher information from quantum metrology to quantify the minimum uncertainty in estimating time. Due to unitarity, the uncertainty in the time estimate does not grow with time if we have access to optimal measurements on the full system. Restricting the measurements to act on a small subsystem or to have low computational complexity leads to results expected from equilibration, where the time uncertainty becomes large at late times. With optimal measurements on a subsystem larger than half of the system, we regain the ability to estimate the time very precisely, even at late times. Hawking's calculation for the reduced density matrix of the black hole radiation in semiclassical gravity contradicts our general predictions for unitary quantum chaotic systems. Hawking's state always has a large uncertainty for attempts to estimate the time using the radiation, whereas our general results imply that the uncertainty should become small after the Page time. This gives a new version of the black hole information loss paradox in terms of the time estimation task. By restricting to simple measurements on the radiation, the time uncertainty becomes large. This indicates from a new perspective that the observations of computationally bounded agents are consistent with the semiclassical effective description of gravity.

Black holes↗
DOE OSTI2024

Variational quantum state preparation for quantum-enhanced metrology in noisy systems

Here, we investigate optimized quantum state preparation for quantum metrology applications in noisy environments. Using the QFI-OPT package, we simulate a low-depth variational quantum circuit (VQC) composed of a sequence of global rotations and entangling operations applied to a chain of qubits that are subject to dephasing noise. The parameters controlling the VQC are numerically optimized to maximize the quantum Fisher information, which characterizes the ultimate metrological sensitivity of a quantum state with respect to a global rotation. We find that, regardless of the details of the entangling operation implemented in the VQC, the optimal quantum states can be broadly classified into a trio of qualitative regimes, i.e., catlike, squeezed like, and product states, associated with different dephasing rates. Our findings are relevant for designing optimal state-preparation strategies for next-generation quantum sensors exploiting entanglement, such as time and frequency standards and magnetometers, aimed at achieving state-of-the-art performance in the presence of noise and decoherence.

quantum Fisher information↗
DOE OSTI2026

Optimal sensing on an asymmetric exceptional surface

We study the connection between exceptional points (EPs) and optimal parameter estimation, in a simple system consisting of two counterpropagating traveling wave modes in a microring resonator. The unknown parameter to be estimated is the strength of a perturbing cross-coupling between the two modes. Partially reflecting the output of one mode into the other creates a non-Hermitian Hamiltonian that exhibits a family of EPs, creating an exceptional surface (ES). We use a fully quantum treatment of field inputs and noise sources to obtain a quantitative bound on the estimation error by calculating the quantum Fisher information (QFI) in the output fields, whose inverse gives the Cramér-Rao lower bound on the mean-squared error of any unbiased estimator. We determine the bounds for two input states, namely, a semiclassical coherent state and a highly nonclassical NOON state. We find that the QFI is enhanced in the presence of an EP for both of these input states and that both states can saturate the Cramér-Rao bound. We then identify idealized yet experimentally feasible measurements that achieve the minimum bound for these two input states. We also investigate how the QFI changes for parameter values that do not lie on the ES, finding that these can have a larger QFI, suggesting alternative routes to optimize the parameter estimation for this problem.

Exceptional points↗