Nonclassical Measurement Research Articles

WE-115. Assessment of classical and non-classical qEEG measures in addicted patients

WE-115. Assessment of classical and non-classical qEEG measures in addicted patients

Statistical Capacity Matters: The Long-Term Effects of Africa’s Slave Trade on Development Reflected by Nighttime Light Intensity

Abstract Empirical research depends on reliable data. Yet, in many countries, statistical agencies do not have the capacity to collect high-quality data on economic development. This is especially the case in Africa, where the capacity to collect such data is affected by the same historical factors that explain economic development—in particular, the slave trade. We hypothesise that the impact of the slave trade on economic development in Africa is biased because cross-country heterogeneity in statistical capacity related to the slave trade creates a non-classical measurement error in gross domestic product (GDP) per capita. Our empirical evidence supports this view. When replacing GDP per capita by nighttime light intensity per capita—an indicator of economic development unrelated to statistical capacity—the impact of the slave trade on economic development drops by a factor of 2–4 depending on model specification and estimation methodology (OLS, IV and high-dimensional sparse models). Various robustness tests further corroborate our main hypothesis.

On the timing of relevant weather conditions in agriculture

AbstractA growing literature is analyzing the effects of weather on agricultural outcomes. In these studies, constructing weather variables requires researchers to define a “season,” a period over which weather conditions are considered relevant to the outcome. We explore the consequences of assuming an incorrect season in such analyses. We show in simulations that imposing an incorrect season introduces nonclassical measurement error in weather regressors, bias in unknown directions. We propose an approach to recover the “true” underlying season and apply it to a US state‐level panel of agricultural Total Factor Productivity. We find that accounting for seasonality can lead to substantially different estimates.

On Non-Convexity of the Nonclassicality Measure via Operator Ordering Sensitivity

In quantum optics, nonclassicality in the sense of Glauber-Sudarshan is a valuable resource related to the quantum aspect of photons. A desirable and intuitive requirement for a consistent measure of nonclassicality is convexity: Classical mixing should not increase nonclassicality. We show that the recently introduced nonclassicality measure [Phys. Rev. Lett. 122, 080402 (2019)] is not convex. This nonclassicality measure is defined via operator ordering sensitivity, which is an interesting and significant probe (witness) of nonclassicality without convexity but can be intrinsically connected to the convex Wigner-Yanase skew information [Proc. Nat. Acad. Sci. United States 49, 910 (1963)] via the square root operation on quantum states. Motivated by the Wigner-Yanase skew information, we also propose a faithful measure of nonclassicality, although it cannot be readily computed, it is convex.

Exploring the limits of the generation of nonclassical states of spins coupled to a cavity by optimal control

We investigate the generation of nonclassical states of spins coupled to a common cavity by means of a collective driving of the spins. We propose a control strategy using specifically designed series of short coherent and squeezing pulses, which have the key advantage of being experimentally implementable with the state-of-the art techniques. The parameters of the control sequence are found by means of optimization algorithms. We consider the cases of two and four spins, the goal being either to reach a well-defined target state or a state maximizing a measure of nonclassicality. We discuss the influence of cavity damping and spin offset on the generation of nonclassical states. We also explore to what extent squeezing fields help to enhance the efficiency of the control process.

Operational resource measure of nonclassicality for number states filtered coherent states

Operational resource measure of nonclassicality for number states filtered coherent states

Panel Regression Models with Non-Classical Measurement Errors: An Application to Investment Equations

Panel Regression Models with Non-Classical Measurement Errors: An Application to Investment Equations

About One Representation-Interpreter of a Monotone Measure

We consider the problem of presenting a nonclassical measure (nonadditive, but monotonous), so-called fuzzy (monotone) measure, by a classical measure, particularly by the Murofushi–Sugeno-type new representation-interpreter. The theorems on the universal interpreter of a monotone (fuzzy) measure in the Choquet integral environment and second-order dual capacities are considered.

Engineering non-classical correlation and teleportation with Robust fidelity using Jaynes–Cummings model

In this paper, we propose a model to describe the geometry of quantum correlations and entanglement through their distinct physical significance in quantum information processing and modern communications. However, geometric discord, using trace, Hilbert–Schmidt distances, and entanglement of formation, is engineered to be a well-defined non-classical correlation measure of an atomic field system. It consists of employing Jaynes–Cummings model to study the interaction between an excited atom at two levels and a single electromagnetic field mode inside an electrodynamic cavity in two cases, namely resonance and non-resonance. In fact, the dynamics of these measures depends decisively on the atom-field initial parameters where, importantly, the field parameters can be specified as control settings to implement an optimal teleportation protocol. The obtained results reveal that the behaviors of teleported geometric quantum discord and entanglement are similar to those displayed for maximum fidelity in terms of fully entanglement fraction. Therefore, since fidelity always exceeds the classical limit, one can design a quantum teleportation scheme with robust fidelity superior to any conventional communication protocol.

Verifying single-mode nonclassicality beyond negativity in phase space

While negativity in phase space is a well-known signature of nonclassicality, a wide variety of nonclassical states require their characterization beyond negativity. We establish a framework of nonclassicality in phase space that addresses nonclassical states comprehensively with a direct experimental evidence. This includes the negativity of phase-space distribution as a special case and further analyzes quantum states with positive distributions effectively. We prove that it detects all nonclassical Gaussian states and all non-Gaussian states of arbitrary dimension remarkably by examining three phase-space points only. Our formalism also provides an experimentally accessible lower bound for a nonclassicality measure based on trace distance. Importantly, this foundational approach can be further adapted to constitute practical tests in two directions looking into particle and wave nature of bosonic systems, via an array of nonideal on-off detectors and coarse-grained homodyne measurement, respectively. All these tests are practically powerful in characterizing nonclasssical states reliably against noise, making a versatile tool for a broad range of quantum systems in quantum technologies.

Measuring Postprandial Metabolic Flexibility to Assess Metabolic Health and Disease

Metabolic abnormalities substantially increase the risk of noncommunicable diseases, which are among the leading causes of mortality globally. Mitigating and preventing these adverse consequences remains challenging due to a limited understanding of metabolic health. Metabolic flexibility, a key tenet of metabolic health, encompasses the responsiveness of interrelated pathways to maintain energy homeostasis throughout daily physiologic challenges, such as the response to meal challenges. One critical underlying research gap concerns the measurement of postprandial metabolic flexibility, which remains incompletely understood. We concisely review the methodology for assessment of postprandial metabolic flexibility in recent human studies. We identify 3 commonalities of study design, specifically the nature of the challenge, nature of the response measured, and approach to data analysis. Primary interventions were acute short-term nutrition challenges, including single- and multiple-macronutrient tolerance tests. Postmeal challenge responses were measured via laboratory assays and instrumentation, based on a diverse set of metabolic flexibility indicators [e.g., energy expenditure (whole-body indirect calorimetry), glucose and insulin kinetics, metabolomics, transcriptomics]. Common standard approaches have been diabetes-centric with single-macronutrient challenges (oral-glucose-tolerance test) to characterize the postprandial response based on glucose and insulin metabolism; or broad measurements of energy expenditure with calculated macronutrient oxidation via indirect calorimetry. Recent methodological advances have included the use of multiple-macronutrient meal challenges that are more representative of physiologic meals consumed by free-living humans, combinatorial approaches for assays and instruments, evaluation of other metabolic flexibility indicators via precision health, systems biology, and temporal perspectives. Omics studies have identified potential novel indicators of metabolic flexibility, which provide greater granularity to prior evidence from canonical approaches. In summary, recent findings indicate the potential for an expanded understanding of postprandial metabolic flexibility, based on nonclassical measurements and methodology, which could represent novel dynamic indicators of metabolic diseases.

The implications of self-reported body weight and height for measurement error in BMI

We designed an experiment to explore the extent of measurement error in body mass index (BMI), when based on self-reported body weight and height. We find that there is a systematic age gradient in the reporting error in BMI, while there is limited evidence of systematic associations with gender, education and income. This is reassuring evidence for the use of self-reported BMI in studies that use it as an outcome, for example, to analyse socioeconomic gradients in obesity. However, our results suggest a complex structure of non-classical measurement error in BMI, depending on both individuals’ and within-household peers’ true BMI. This may bias studies that use BMI based on self-reported data as a regressor. We also observe non-classical reporting error in height and weight — taller people seem to report their height more accurately, while a nonlinear relationship is evident for weight, with a sharper increase in reporting errors for those of greater weight. Common methods to mitigate reporting error in BMI using predictions from corrective equations do not fully eliminate reporting heterogeneity associated with individual and within-household true BMI. Overall, the presence of non-classical error in BMI highlights the importance of collecting measured body weight and height data in large social science datasets.

Entanglement-enhanced estimation of a parameter embedded in multiple phases

Quantum-enhanced sensing promises to improve the performance of sensing tasks using non-classical probes and measurements that require far fewer scene-modulated photons than the best classical schemes, thereby granting previously-inaccessible information about a wide range of physical systems. We propose a generalized distributed sensing framework that uses an entangled quantum probe to estimate a scene-parameter encoded within an array of phases, with a functional dependence on that parameter determined by the physics of the actual system. The receiver uses a laser light source enhanced by quantum-entangled multi-partite squeezed-vacuum light to probe the phases and thereby estimate the desired scene-parameter. The entanglement suppresses the collective quantum vacuum noise across the phase array. We report simple analytical expressions for the Cram\'er Rao bound that depend only on the optical probes and the physical model of the measured system, and we show that our structured receiver asymptotically saturates the quantum Cram\'er-Rao bound in the lossless case. Our approach enables Heisenberg limited precision in estimating a scene-parameter with respect to total probe energy, as well as with respect to the number of modulated phases. Furthermore, we study the impact of uniform loss in our system and examine the behavior of both the quantum and the classical Cram\'er-Rao bounds. We apply our framework to examples as diverse as radio-frequency phased-array directional radar, beam-displacement tracking for atomic-force microscopy, and fiber-based temperature gradiometry.

A simple test of completeness in a class of nonparametric specification

This paper provides a test for completeness in a class of nonparametric specification with an additive and independent error term. It is known that such a nonparametric location family of functions is complete if and only if the characteristic function of the error term has no zeros on the real line. Because a zero of the error characteristic function implies that of an observed marginal distribution, we propose a simple test for zeros of characteristic function of the observed distribution, in which rejection of the null hypothesis implies the completeness. This test is applicable to many popular settings, such as nonparametric regression models with instrumental variables, and nonclassical measurement error models. We describe the asymptotic behavior of the tests under the null and alternative hypotheses and investigate the finite sample properties of the proposed test through a Monte Carlo study. We illustrate our method empirically by estimating a measurement error model using the CPS/SSR 1978 exact match file.

Analysis of planes within reduced micromorphic model

A plane within reduced micromorphic model subjected to external static load is studied using the finite element method. The reduced micromorphic model is a generalized continuum theory which can be used to capture the interaction of the microstructure. In this approach, the microstructure is homogenized and replaced by a reduced micromorphic material model. Then, avoiding the complexity of the microstructure, the reduced micromorphic model is analyzed to reveal the interaction of the microstructure and the external loading. In this study, the three-dimensional formulation of the reduced micromorphic model is dimensionally reduced to address a plane under in-plane external load. The governing system of partial differential equations with corresponding consistent boundary conditions are discretized and solved using the finite element method. The classical and nonclassical deformation measures are then demonstrated and discussed for the first time for a material employing the reduced micromorphic model.

On the computation of recurrence coefficients for univariate orthogonal polynomials.

Associated to a finite measure on the real line with finite moments are recurrence coefficients in a three-term formula for orthogonal polynomials with respect to this measure. These recurrence coefficients are frequently inputs to modern computational tools that facilitate evaluation and manipulation of polynomials with respect to the measure, and such tasks are foundational in numerical approximation and quadrature. Although the recurrence coefficients for classical measures are known explicitly, those for nonclassical measures must typically be numerically computed. We survey and review existing approaches for computing these recurrence coefficients for univariate orthogonal polynomial families and propose a novel "predictor-corrector" algorithm for a general class of continuous measures. We combine the predictor-corrector scheme with a stabilized Lanczos procedure for a new hybrid algorithm that computes recurrence coefficients for a fairly wide class of measures that can have both continuous and discrete parts. We evaluate the new algorithms against existing methods in terms of accuracy and efficiency.

Identification of nonparametric monotonic regression models with continuous nonclassical measurement errors

This paper provides sufficient conditions for identification of a nonparametric regression model with an unobserved continuous regressor subject to nonclassical measurement error. The measurement error may be directly correlated with the latent regressor in the model. Our identification strategy does not require the availability of additional data information, such as a secondary measurement, an instrumental variable, or an auxiliary sample. Our main assumptions for nonparametric identification include monotonicity of the regression function, independence of the regression error, and completeness of the measurement error distribution. We also propose a sieve maximum likelihood estimator and investigate its finite sample property through Monte Carlo simulations.

Quantum nanophotonic and nanoplasmonic sensing: towards quantum optical bioscience laboratories on chip

Abstract Quantum-enhanced sensing and metrology pave the way for promising routes to fulfil the present day fundamental and technological demands for integrated chips which surpass the classical functional and measurement limits. The most precise measurements of optical properties such as phase or intensity require quantum optical measurement schemes. These non-classical measurements exploit phenomena such as entanglement and squeezing of optical probe states. They are also subject to lower detection limits as compared to classical photodetection schemes. Biosensing with non-classical light sources of entangled photons or squeezed light holds the key for realizing quantum optical bioscience laboratories which could be integrated on chip. Single-molecule sensing with such non-classical sources of light would be a forerunner to attaining the smallest uncertainty and the highest information per photon number. This demands an integrated non-classical sensing approach which would combine the subtle non-deterministic measurement techniques of quantum optics with the device-level integration capabilities attained through nanophotonics as well as nanoplasmonics. In this back drop, we review the underlining principles in quantum sensing, the quantum optical probes and protocols as well as state-of-the-art building blocks in quantum optical sensing. We further explore the recent developments in quantum photonic/plasmonic sensing and imaging together with the potential of combining them with burgeoning field of coupled cavity integrated optoplasmonic biosensing platforms.

Analyzing Subjective Well-Being Data with Misclassification

We use novel nonparametric techniques to test for the presence of nonclassical measurement error in reported life satisfaction (LS) and study the potential effects from ignoring it. Our dataset comes from Wave 3 of the UK Understanding Society that is surveyed from 35,000 British households. Our test finds evidence of measurement error in reported LS for the entire dataset as well as for 26 out of 32 socioeconomic subgroups in the sample. We estimate the joint distribution of reported and latent LS nonparametrically in order to understand the mis-reporting behavior. We show this distribution can then be used to estimate parametric models of latent LS. We find measurement error bias is not severe enough to distort the main drivers of LS. But there is an important difference that is policy relevant. We find women tend to over-report their latent LS relative to men. This may help explain the gender puzzle that questions why women are reportedly happier than men despite being worse off in objective outcomes such as income and employment.

Can we control the amount of useful nonclassicality in a photon added hypergeometric state?

Non-Gaussianity inducing operations are studied in the recent past from different perspectives. Here, we study the role of photon addition, a non-Gaussianity inducing operation, in the enhancement of nonclassicality in a finite dimensional quantum state, namely hypergeometric state with the help of some quantifiers and measures of nonclassicality. We observed that measures to characterize the quality of single photon source and anticlassicality lead to the similar conclusion, i.e. to obtain the desired quantum features one has to choose all the state parameters such that average photon numbers remains low. Wigner logarithmic negativity of the photon added hypergeometric state and concurrence of the two-mode entangled state generated at the output of a beamsplitter from this state show that nonclassicality can be enhanced by increasing the state parameter and photon number addition but decreasing the dimension of the state. In principle, decreasing the dimension of the state is analogous to holeburning and is thus expected to increase nonclassicality. Further, the variation of Wigner function not only qualitatively illustrates the same features as observed quantitatively through concurrence potential and Wigner logarithimic negativity, but illustrate non-Gaussianity of the quantum state as well.