Physical Assumptions Research Articles

Quantum thermalization via multiwave mixing

We discuss thermalization in a multimode quantum cavity under unitary evolution. According to general principles, an isolated system with quadratic couplings does not exhibit thermalization. However, we find that nonlinearities, here three-wave perturbation, typical for instance in superconducting Josephson systems, may lead to thermalization into a Bose-Einstein distribution of occupations of the modes. The temperature of this state is dictated by energy conservation in this closed system, and the thermal distribution is robust against weak disturbances. We discuss how our findings open up new avenues to experimentally probe fundamental assumptions of statistical physics in solid-state systems. Published by the American Physical Society 2024

What is it like to be unitarily reversed?

There has been in recent years a huge surge of interest in the so-called extended Wigner’s friend scenario (EWFS). In short, a series of theorems (with some variation in detail) puts pressure on the ability of different agents in the scenario to account for each of the others’ measured outcomes: the outcomes cannot be assigned single well-defined values while also satisfying other reasonable physical assumptions. These theorems have been interpreted as showing that there can be no absolute, third-person, ‘God’s eye’ description of our reality. The focus of this paper is the strongest of these no-go theorems, the ‘local friendliness’ theorem of Bong et al. (2020, Nature Physics, 16, 1199–1205), which gives earnest consideration to the possibility of a measurement that unitarily reverses an entire lab system, including a conscious agent, thereby erasing the agent’s memory. The purpose of this paper is to begin the philosophical conversation regarding key questions concerning this process: Are the events in the lab merely ‘erased’, or do they in some sense not exist at all? What would it be like to be unitarily reversed? Should an agent care about any experiences they have inside the lab before they are reversed? This analysis employs a parallel case of memory erasure, to which this case can be contrasted, arising in the context of drug-induced amnesia as a result of administering anaesthesia during medical procedures (Carbonell, 2014, Bioethics, 28(5), 245–254). I argue that the consequences of unitarily reversing an agent are much more dramatic than simply memory erasure—the set of events themselves, and the personal timeline of the agent, leave no record at all inside or outside the lab. I consider the ramifications of this for the picture of reality that arises from the EWFS.

Novel results from quadratically nonlinear elastic wave models using Murnaghan’s potential

AbstractIn this article, we study one, two and three-dimensional nonlinear elastic wave equations using quadratically nonlinear Murnaghan potential. We employ two effective methods for obtaining approximate series solutions the Adomian decomposition and the variational iteration method. These methods have the advantage of not requiring any physical parametric assumptions in the problem. Finally, these methods can generate expansion solutions for linear and nonlinear differential equations without perturbation, linearization, or discretization. The results obtained using the adopted methods along various initial and boundary conditions are in excellent agreement with the numerical results on MATLAB, which show the reliability of our methods to these problems. We came to the conclusion that our methods are accurate and simple to use.

Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)

We show how a complete mathematical model of a physical process can be learned directly from data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality and symmetry, a weak formulation of differential equations and sparse regression. To illustrate this, we extract a complete system of governing equations of fluid dynamics – the Navier–Stokes equation, the continuity equation and the boundary conditions – as well as the pressure-Poisson and energy equations, from numerical data describing a highly turbulent channel flow in three dimensions. Whether they represent known or unknown physics, relations discovered using this approach take the familiar form of partial differential equations, which are easily interpretable and readily provide information about the relative importance of different physical effects. The proposed approach offers insight into the quality of the data, serving as a useful diagnostic tool. It is also remarkably robust, yielding accurate results for very high noise levels, and should thus be well suited for analysis of experimental data.

Three-dimensional Darcy-Forchheimer modelling of MHD hybrid nanofluid over rotating stretching/shrinking surface with Hamilton-Crosser and Yamada-Ota conductivity models

Instead of single nanoparticles, the combined effects of more than one solid nanoparticle have presented wide range of real-word application in several engineering as well as biomedical areas. The present analysis brings out a combined effect of Hamilton-Crosser and Yamada-Ota thermal conductivity models for the magnetohydrodynamic flow of hybridised fluid vi a rotating stretching/shrinking surface. The hybridised fluid comprised of silver and molybdenum tetrasulphide nanoparticle in association with the effect of Joule heating enriches the flow properties. Additionally, the Darcy-Forchheimer inertial drag with the impose of thermal radiation affecting the flow as well as heat transfer properties. The proposed mathematical model equipped with physical assumptions is transmuted into dimensionless form by utilizing similarity functions. Further, the traditional numerical technique is taken care of for the solution of the transmuted model equipped with diversified factors. The important characteristic of several factors are deployed graphically affecting various flow profiles. Finally, the outstanding features explored in the proposed investigation are stated as below; the comparative analysis reveals that, the heat transport properties became advanced in case of Hamilton-Crosser model rather than the Yamada-Ota conductivity model. However, the heat transportation rate is controlled by the increasing Eckert number but thermal radiation enhances it significantly.

Revisiting empirical solar energetic particle scaling relations

Aims. The space radiation environment conditions and the maximum expected coronal mass ejection (CME) speed are assessed by investigating scaling laws between the peak proton flux and fluence of solar energetic particle (SEP) events with the speed of the CMEs. Methods. We used a complete catalog of SEP events, covering the last ∼25 years of CME observations (i.e., 1997–2017). We calculated the peak proton fluxes and integrated event fluences for events that reached an integral energy of up to E > 100 MeV. For a sample of 38 strong SEP events, we first investigated the statistical relations between the recorded peak proton fluxes (IP) and fluences (FP) at a set of integral energies of E > 10 MeV, E > 30 MeV, E > 60 MeV, and E > 100 MeV versus the projected CME speed near the Sun (VCME) obtained by the Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph (SOHO/LASCO). Based on the inferred relations, we further calculated the integrated energy dependence of both IP and FP, assuming that they follow an inverse power law with respect to energy. By making use of simple physical assumptions, we combined our derived scaling laws to estimate the upper limits for VCME, IP, and FP by focusing on two cases of known extreme SEP events that occurred on 23 February 1956, (GLE05) and in AD774/775, respectively. Based on the physical constraints and assumptions, several options for the upper limit VCME associated with these events were investigated. Results. A scaling law relating IP and FP to the CME speed as VCME5 for CMEs ranging between ∼3400–5400 km/s is consistent with values of FP inferred for the cosmogenic nuclide event of AD774/775. At the same time, the upper CME speed that the current Sun can provide possibly falls within an upper limit of VCME ≤ 5500 km/s.

Predicting gravitational wave signals from BPASS White Dwarf Binary and Black Hole Binary populations of a Milky Way-like galaxy model for LISA

Abstract Galactic white dwarf binaries (WDBs) and black hole binaries (BHBs) will be gravitational wave (GW) sources for LISA. Their detection will provide insights into binary evolution and the evolution of our Galaxy through cosmic history. Here, we make predictions of the expected WDB and BHB population within our Galaxy. We combine predictions of the compact remnant binary populations expected by stellar evolution from the detailed Binary Population and Spectral Synthesis (BPASS) code, with a Milky Way analogue galaxy model from the Feedback In Realistic Environment (FIRE) simulations. We use PhenomA and legwork to simulate LISA observations. Both packages make similar predictions that on average four Galactic BHBs and 673 Galactic WDBs are above the signal-to-noise ratio (SNR) threshold of 7 after a four-year mission. We compare these predictions to earlier results using the Binary Star Evolution (BSE) code with the same FIRE model galaxy. We find that BPASS predicts a few more LISA observable Galactic BHBs and a twentieth of the Galactic WDBs. The differences are due to the different physical assumptions that have gone into the binary evolution calculations. These results indicate that the expected population of compact binaries that LISA will detect depends very sensitively on the binary population synthesis models used and thus observations of the LISA population will provide tight constraints on our modelling of binary stars. Finally, from our synthetic populations we have created mock LISA signals that can be used to test and refine data processing methods of the eventual LISA observations.

Three-Dimensional Nonlocal Thermodynamic Equilibrium Abundance Analyses of Late-Type Stars

The chemical compositions of stars encode the history of the universe and are thus fundamental for advancing our knowledge of astrophysics and cosmology. However, measurements of elemental abundance ratios, and our interpretations of them, strongly depend on the physical assumptions that dictate the generation of synthetic stellar spectra. Three-dimensional radiation-hydrodynamic (3D RHD) box-in-a-star simulations of stellar atmospheres offer a more realistic representation of surface convection occurring in late-type stars than do traditional one-dimensional (1D) hydrostatic models. As evident from a multitude of observational tests, the coupling of 3D RHD models with line formation in nonlocal thermodynamic equilibrium (non-LTE) today provides a solid foundation for abundance analysis for many elements. This review describes the ongoing and transformational work to advance the state of the art and replace 1D LTE spectrum synthesis with its 3D non-LTE counterpart. In summary: ▪3D and non-LTE effects are intricately coupled, and consistent modeling thereof is necessary for high-precision abundances; such modeling is currently feasible for individual elements in large surveys. Mean 3D (〈3D〉) models are not adequate as substitutes.▪The solar abundance debate is presently dominated by choices and systematic uncertainties that are not specific to 3D non-LTE modeling.▪3D non-LTE abundance corrections have a profound impact on our understanding of FGK-type stars, exoplanets, and the nucleosynthetic origins of the elements.

Enhanced heat transfer in novel star-shaped enclosure with hybrid nanofluids: A neural network-assisted study

The current research is a numerical investigation of the thermo-fluidic transport trend within a new star-shaped enclosure filled with Fe3O4−MWCNT (Multiwall Carbon Nanotubes) suspended hybrid nanoparticles in a base fluid (water), induced by a horizontal magnetizing field. A rectangular rod inside the cavity positioned at center is kept at a high temperature, as the low temperature is chosen for outer corrugated boundary. Formulation yelled in mathematical principles, along with the boundary conditions and some physical assumptions, are formulated as dimensionless PDEs. The finite element method (FEM) assisted by “COMSOL” software, employed for numerical simulations, and the PARDISO solver is used for solving nonlinear system of equations. Also, an artificial neural network (ANN) model is assembled to analyze the effect of these parameters on thermal and flow transport properties of Hybrid nanofluid. The training of this ANN model is done by a dataset generated from numerical simulations, suggesting predictions regarding heat transport under varying parameters. This approach does not only reduce the effort, but also reduces computing time when exploring the thermal behaviors across various datasets. The visualization of velocity and temperature fields through streamlines and isotherms, along with the evaluation of the Nusselt number, illustrate the enhanced heat transfer facilitated by the incorporation of Fe3O4−MWCNT nanoparticles. The results show that increased magnetic field strength reduces fluid velocity due to the generated Lorentz force, which counteracts convective flow. Percentage analysis indicates that hybrid nanofluids (Fe3O4−MWCNT) significantly improve thermal distribution compared to conventional fluids. This study demonstrates the effectiveness of ANN models in forecasting the influence of diverse factors on the flow and heat transport characteristics of hybrid nanofluids. These insights are essential to the design and optimization of heat transfer systems.

Analysis of entropy generation and MHD thermo‐solutal convection flow of Ellis nanofluid through inclined microchannel

AbstractThis study investigates heat, mass transport, and entropy production in Ellis nanofluid flow through an inclined permeable microchannel, considering Navier's slip effects with convective boundary conditions. It incorporates nanoparticle's thermophoresis and Brownian motion effects under a transverse magnetic field, with fluid suction and injection at microchannel walls. Under appropriate physical assumptions, the problem is presented as nonlinear ordinary differential equations, which are later nondimensionalized. The MATLAB bvp4c solver is used for numerical solutions of the transformed equations. Graphical depictions in the study illustrate how various factors influence velocity, temperature, concentration, Bejan number, and entropy generation. Engineering parameters, affected by changes in critical factors, are presented in tabular format, including the skin friction coefficient, Nusselt number, and Sherwood number. Notably, the enhancement in Ellis fluid parameter has a dual effect, enhancing velocity and Bejan number in the microchannel's lower half, while reversing in the upper half. For the increment in Ellis parameter, the impact on Bejan number for 0.5 is significant and the effect on entropy production contrasts with that of Bejan number. This research offers practical insights for designing efficient microfluidic heat exchangers and developing advanced nanofluids for improved thermal performance while minimizing entropy generation. Additionally, it underscores the potential for innovation within the domain of microfluidics and nanomaterial‐driven heat transfer systems. Furthermore, it should be noted that the flow behavior of Ellis nanofluids within microchannels can closely replicate natural flow patterns found in biological systems, offering insights that could have numerous applications in biology and related fields.

Neural network-based hybrid modeling approach incorporating Bayesian optimization with industrial soft sensor application

Hybrid modeling combines physical and data-driven models to improve the performance of industrial soft sensors. However, simplified physical assumptions and extensive parameter optimization increase the complexity of the model and decrease its robustness and accuracy. In this study, a novel neural network-based approach for hybrid modeling was developed, based on Runge-Kutta (RK) and Bayesian hyperparameter optimization. First, the recursive solution equation for the quality variable was derived using the master equation, which included the black-box term and RK method. Second, the numerical solution of the black-box term was inverted using the derived equation as a label for the training samples, and hyperparameters were optimized using Bayesian optimization. Finally, during the prediction phase, quality variables at subsequent times were derived by solving a recursive equation containing neural network approximations. The superiority of the proposed soft sensing method was assessed through studies on a continuous stirred tank reactor (CSTR) case and a simulated penicillin case. The experimental findings demonstrate that the proposed method is better than existing methods in terms of robustness and accuracy.

Modeling non-spherical hailstones

Abstract Hail research and forecasting models necessarily involve explicit or implicit – and uncertain – physical assumptions regarding hailstones’ shape, tumbling behavior, fallspeed, and thermal energy transfer. Whereas most models assume spherical hailstones, we relax this assumption by using hailstone shape data from field observations to establish empirical size-shape relationships with reasonable degrees of randomness considering hailstones’ natural shape variability, capturing the observed distribution of tri-axial ellipsoidal shapes. We also incorporate explicit, random tumbling of individual hailstones during their growth to simulate their free-falling behavior and the resultant changes in cross-sectional area (which affects growth by hydrometeor collection.) These physical attributes are incorporated in calculating hailstones’ fallspeeds, using either empirical or analytical relationships based on each hailstone’s Best and Reynolds numbers. Options for drag coefficient modification are added to emulate hailstones’ rough surfaces (lobes), which then modifies their thermal energy and vapor exchange with the environment. We investigate how applying these physical assumptions about nonspherical hail into the Penn State hail growth trajectory model, coupled with Cloud Model 1 supercell simulations, impacts hail production, and examine the reasons behind the resulting variability in hail statistics. The choice of hailstone size-mass relation and fallspeed scheme have the strongest influence on hail sizes. Using non-spherical, tumbling hailstones reduces the number of large hailstones produced. Applying shape-specific thermal energy transfer coefficients subtly increases sizes; the effects of lobes vary depending on the fallspeed scheme used. These physical assumptions, although adding complexity to modeling, can be parameterized efficiently and potentially used in microphysics schemes.

Minimal model identification of drum brake squeal via SINDy

The industrial standard in the design and development process of NVH(Noise Vibration Harshness) characteristic of brakes is the application of Finite Element(FE) models with a high number of degrees of freedom in the range of one or several millions. Nevertheless, parallel experimental investigations are still indispensable. On the other hand, minimal models with, due to the inclusion of the self-excitation process, at least two degrees of freedom are well known to be capable to explain qualitatively phenomena as instability of the desired non-vibrating solution or limit cycle oscillation but are in general very inaccurate in predicting the dynamics of a specific real brake. This is because the underlying physical assumptions are already too restrictive and model parameters (especially those referring to nonlinearities) are widely unknown. To overcome this problem, the data-driven modeling approach SINDy(Sparse Identification of Nonlinear Dynamics) is applied to identify appropriate nonlinear functions for a brake squeal minimal model. A problem thereby is the limited database. It turns out that the naive implementation of the method yielding the lowest possible residuum does not necessarily provide physically meaningful models and results, respectively. Instead, a constrained model that incorporates physical knowledge is used to robustly identify parameters and reproduce realistic dynamic behavior. Thereby, several appropriate models with coexisting limit cycles and stationary equilibrium are identified. In particular, it was found that the angular position of the brake drum has a significant influence on the model parameters and therefore must be taken into account in a model with long-term validity.

Modeling of fluid‐rigid body interaction in an electrically conducting fluid

AbstractWe derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical assumptions under which a mathematical analysis of the model becomes feasible. Our main focus lies on the derivation of the boundary and interface conditions for the electromagnetic fields as well as the derivation of the magnetohydrodynamic approximation carried out via a nondimensionalization of the system.

Physical properties of InxSey and CuInSe2 thin films with potential application in radiation detectors

A study of InxSey and CuInSe2 thin films processed by the thermal co-evaporation technique by evaluating its physical properties is carried out. Both InxSey as well as CuInSe2 thin films were synthesized by multi-source thermal co-evaporation technique, using Knudsen-type effusion cells. The optical, structural, electrical, and morphological properties of each film were analyzed in order to determine the feasibility at the formation of a p-CuInSe2/n-InxSey heterojunction. InxSey films exhibited bandgap values in the range of 2.4–2.7 eV which was determined by UV–vis spectroscopic analysis. Vibrational modes associated to In2Se3 as well as Se are presented in the InxSey films according to Raman studies. The irregular morphology of the grains on the InxSey surface, with an average size of 380 nm are related to both In2Se3 and Se materials according to Raman spectroscopy and Scanning Electron Microscopy analysis. The InxSey thin films showed resistivity vales around 10–3 Ω·cm. The Hackee´s figure of Merit (FOMH) analysis supported the physical assumption that InxSey thin films are feasible to be used as window layer in a photovoltaic device because of the high values of FOMH obtained for samples processed at 300 °C. On the other hand, an influence on the morphology of the CuInSe2 films was observed when the films were synthetized at different substrate temperature. Uniform CuInSe2 films with agglomerated cauliflower-like grains with an average size of 1.8 μm were observed by SEM. The presence of binary phases within the CuInSe2 compound were detected through Raman and x-ray characterization. Average crystallite size of 61 nm and microstrain around 2.5 × 10–3 were estimated for the CuInSe2 films through x-ray analysis. According to the physical properties analyzed the InxSey/CuInSe2 semiconductor bilayer can be a suitable candidate for application in photovoltaic devices as well as charged particle detector.

Measuring Residual Stresses with Crack Compliance Methods: An Ill-Posed Inverse Problem with a Closed-Form Kernel

By means of relaxation methods, residual stresses can be obtained by introducing a progressive cut or a hole in a specimen and by measuring and elaborating the strains or displacements that are consequently produced. If the cut can be considered a controlled crack-like defect, by leveraging Bueckner’s superposition principle, the relaxed strains can be modeled through a weighted integral of the residual stress relieved by the cut. To evaluate residual stresses, an integral equation must be solved. From a practical point of view, the solution is usually based on a discretization technique that transforms the integral equation into a linear system of algebraic equations, whose solutions can be easily obtained, at least from a computational point of view. However, the linear system is often significantly ill-conditioned. In this paper, it is shown that its ill-conditioning is actually a consequence of a much deeper property of the underlying integral equation, which is reflected also in the discretized setting. In fact, the original problem is ill-posed. The ill-posedness is anything but a mathematical sophistry; indeed, it profoundly affects the properties of the discretized system too. In particular, it induces the so-called bias–variance tradeoff, a property that affects many experimental procedures, in which the analyst is forced to introduce some bias in order to obtain a solution that is not overwhelmed by measurement noise. In turn, unless it is backed up by sound and reasonable physical assumptions on some properties of the solution, the introduced bias is potentially infinite and impairs every uncertainty quantification technique. To support these topics, an illustrative numerical example using the crack compliance (also known as slitting) method is presented. The availability of the Linear Elastic Fracture Mechanics Weight Function for the problem allows for a completely analytical formulation of the original integral equation by which bias due to the numerical approximation of the physical model is prevented.

Inferring intrahalo light from stellar kinematics. A deep learning approach

In the context of structure formation, disentangling the central galaxy stellar population from the stellar intrahalo light can help us shed light on the formation history of the halo as a whole, as the properties of the stellar components are expected to retain traces of the formation history. Many approaches are adopted to assess the task, depending on different physical assumptions (e.g. the light profile, chemical composition, and kinematical differences) and depending on whether the full six-dimensional phase-space information is known (much like in simulations) or whether one analyses projected quantities (i.e. observations). This paper paves the way for a new approach to bridge the gap between observational and simulation methods. We propose the use of projected kinematical information from stars in simulations in combination with deep learning to create a robust method for identifying intrahalo light in observational data to enhance understanding and consistency in studying the process of galaxy formation. Using deep learning techniques, particularly a convolutional neural network called U-Net, we developed a methodology for predicting these contributions in simulated galaxy cluster images. We created a sample of mock images from hydrodynamical simulations (including masking of the interlopers) to train, validate and test the network. Reinforced training (Attention U-Net) was used to improve the first results, as the innermost central regions of the mock images consistently overestimate the stellar intrahalo contribution. Our work shows that adequate training over a representative sample of mock images can lead to good predictions of the intrahalo light distribution. The model is mildly dependent on the training size and its predictions are less accurate when applied to mock images from different simulations. However, the main features (spatial scales and gradients of the stellar fractions) are recovered for all tests. While the method presented here should be considered as a proof of concept, future work (e.g. generating more realistic mock observations) is required to enable the application of the proposed model to observational data.

Estimating the cost and affordability of healthy diets: How much do methods matter?

Recently developed cost and affordability of healthy diet (CoAHD) metrics have quickly become mainstream food security indicators. However, published research on the sensitivity of estimation methods is limited. This paper focuses on two important innovations in CoAHD measurement at the global level. First, we develop a demographic scaling factor to adjust healthy diet costs for cross-country differences in age structures, since younger populations generally require fewer calories than older populations. Second, we improve the way in which household expenditure available for purchasing food (“food budgets”) are derived. In addition, we explore sensitivity of global CoAHD estimates to potential problems with the representativeness and food product coverage of global food price data and vary assumptions for activity levels that shape energy expenditure requirements. We apply these explorations to the EAT-Lancet reference diet in 137 countries using price data from 2017. Relative to the conventional methods, we find that demographic scaling and improved food budget derivation substantially reduces the estimated population who cannot afford a healthy diet, from 3.02 to 2.13 billion. Adjustments for low product coverage can lead to modest reductions for specific regions and food groups, while higher physical activity assumptions increase the share of people who cannot afford a healthy diet, though perhaps implausibly so. Methods clearly matter in CoAHD estimation, and more accurate and timelier CoAHD estimates have substantial scope to improve policy analysis, design and targeting.

Quantum force sensing by digital twinning of atomic Bose-Einstein condensates

High sensitivity detection plays a vital role in science discoveries and technological applications. While intriguing methods utilizing collective many-body correlations and quantum entanglements have been developed in physics to enhance sensitivity, their practical implementation remains challenging due to rigorous technological requirements. Here, we propose an entirely data-driven approach that harnesses the capabilities of machine learning, to significantly augment weak-signal detection sensitivity. In an atomic force sensor, our method combines a digital replica of force-free data with anomaly detection technique, devoid of any prior knowledge about the physical system or assumptions regarding the sensing process. Our findings demonstrate a significant advancement in sensitivity, achieving an order of magnitude improvement over conventional protocols in detecting a weak force of approximately 10−25N. The resulting sensitivity reaches 1.7(4)×10−25N/Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.7(4)\ imes 1{0}^{-25}\\,{{{{{{{\\rm{N}}}}}}}}/\\sqrt{{{{{{{{\\rm{Hz}}}}}}}}}$$\\end{document}. Our machine learning-based signal processing approach does not rely on system-specific details or processed signals, rendering it highly applicable to sensing technologies across various domains.

Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios

Self-testing is a promising approach to certifying quantum states or measurements. Originally, it relied solely on the outcome statistics of the measurements involved in a device-independent (DI) setup. Extra physical assumptions about the system make the setup semi-DI. In the latter approach, we consider a prepare-and-measure scenario in which the dimension of the mediating particle is assumed to be two. In a setup involving four (three) preparations and three (two) projective measurements in addition to the target, we exemplify how to self-test any four- (three-) outcome extremal positive operator-valued measure using a linear witness. One of our constructions also achieves self-testing of any number of states with the help of as many projective measurements as the dimensionality of the space spanned by the corresponding Bloch vectors. These constructions are conjectured to be minimal in terms of the number of preparations and measurements required. In addition, we implement one of our prepare-and-measure constructionson IBM and IonQ quantum processors and certify the existence of a complex qubit Hilbert space based on the data obtained from these experiments.