State Values Research Articles

Developing a utility value set for the Gambling Quality of Life Scale-Brief (GQoLS-Brief) using a discrete choice experiment.

The Gambling Quality of Life Scale -brief (GQoLS-Brief) assesses the impact of gambling disorder (GD) on quality of life (QoL). Preference-based measures are essential for obtaining the quality adjustment weight (i.e. utility score) needed to calculate quality-adjusted life years (QALYs) in economic evaluations. We aimed to derive a value set for the GQoLS-Brief. We employed a discrete choice experiment for preference elicitation. An online survey was administered (n = 928). Respondents completed 10 choice tasks, each presenting two GQoLS-Brief health states alongside life expectancy. Conditional logit regression, parameterized to fit the QALY framework, was used for data analysis. QALY weights for each health state defined by the GQoLS-Brief were calculated. The estimated coefficients from the conditional logit models aligned with expectations: utility increased with survival time and decreased with QoL impairment. Utility values for health states ranged from -1.48 (worse than death) to 1.0. "Financial difficulties" exhibited the highest utility decrement, followed by "Sleep disturbance related to financial difficulties." This reference set facilitates the calculation of QALYs for economic evaluations of GD interventions. The weight of subjective financial difficulties underscores the need for therapeutic interventions to target this aspect.

Critical success factors for circular economy implementation toward sustainable construction: an iterative stationary approach

ABSTRACTS The continuous depletion of natural resources, coupled with negative environmental impacts and increasing costs of construction projects, has drawn the attention of stakeholders in the construction industry to the circular economy (CE) concept. Over the past decade, the investigations of CE have increased significantly. Yet, this is not the case for developing countries, where the CE practice is still in an infant stage. This paper explores the critical success factors (CSFs) in order to advance knowledge of the implementation of CE in the Nigerian construction industry. The CSFs were compiled from previous studies and subsequently reviewed and classified through a semi-structured interview. A questionnaire survey consisting of the CSFs was subsequently sent to the construction professionals for their response. The relative importance index was further employed to determine the significant factors within each group. In this paper, an iterating stationary approach was adopted to further examine the factors by using Ginni's mean measure of dispersion to create a uniform weight for the index numbers. The Lebesgue integral measure to the mean value was used to provide a value range within the relative importance index (RII). This technique evaluated the impacts of the CE CSFs on the Nigerian construction industry. The results indicate a geometric mean stationary value of 0.7040, which signifies that the CSFs for CE implementation in the Nigerian construction industry are alleviating the fragmented construction industry through the stakeholder’s collaboration having the RII value of 0.71, and the availability of technologies for end of the life management of buildings with the RII value of 0.7.

Minimal clinically important difference in the Japanese Orthopedic Association Score and shoulder 36 after arthroscopic rotator cuff repair in a Japanese population: A retrospective cohort study

BackgroundIn Japan, the Japanese Orthopedic Association (JOA) score is widely used as a clinician-reported outcome after shoulder surgery. However, Shoulder36 is positioned as a general patient-reported outcome measure. This study aimed to determine the correlations between the JOA score and scores in the domains of the Shoulder36 and their minimal clinically important differences (MCIDs) and cutoff values for the patient-acceptable symptom state (PASS) after unilateral arthroscopic rotator cuff repair (ARCR). MethodsWe evaluated 145 patients using the JOA score and Shoulder36 before and 1 year after surgery. The MCID and PASS cutoff values were determined by patients’ responses to the following anchor item: A, none (“no good at all”); B, poor (“some effect but unsatisfactory”); C, good (“satisfactory effect with occasional episodes of pain or stiffness”); D, excellent (“ideal response, virtually pain-free”). The correlations between the JOA score and the domains of the Shoulder36 were statistically calculated. The border between B and C was defined as the threshold for PASS. ResultsThere were significant correlations between the JOA score and the Shoulder36 domains. The responses to the anchor item were as follows: A (n = 0), B (n = 21), C (n = 76), and D (n = 48). The MCID for the JOA score was 19.5 points and the MCIDs for Shoulder36 were 0.5 points for pain, 0.667 for range of motion, 0.67 for muscle strength, 0.3 for general health, 0.571 for activities of daily living, and 1.0 for sports ability. The PASS cutoff value was 89.0 points for the JOA score and 3.8 points for pain, 3.667 for range of motion, 3.0 for muscle strength, 3.7 for general health, 3.7 for activities of daily living, and 3.0 for sports ability in the Shoulder36. ConclusionsThe MCID and cutoff PASS values for the JOA score and Shoulder36 identified in this study will help to determine the effectiveness of multidisciplinary management after ARCR.

On exact observability of a nonlinear evolutionary equation with a bounded right-hand side operator on a small interval

For the Cauchy problem associated with a nonlinear ordinary differential equation in a Hilbert space $X$, we obtain sufficient conditions for exact observability on a small interval. By means of the condition of boundedness from below by a positive constant on the unit sphere with respect to a linear observer (observation operator) and with the help of Minty–Browder's theorem, the observability problem is reformulated as an operator (integral) equation with the right-hand side involving (in addition to the Volterra-type term, which is “local” in time) a nonlocal term as well. The unique solvability of the obtained operator equation (the equation of state reconstruction from observation) is proved with the help of the contraction map principle and the hypothesis about smallness of the observation interval. Moreover, we prove two theorems on global reconstruction of a state: 1) from observation on a small interval and under the condition of global solvability of some majorant integral equation in the space $\mathbb{R}$; 2) from a series of observations on small intervals in the presence of a priori information on the belonging of the state values to a bounded ball in $X$. As an example (of an independent interest), a semilinear equation of the global electric circuit in the Earth's atmosphere is considered.

The best indices of anesthesia depth monitored by electroencephalogram in different age groups

Introduction Current electroencephalogram (EEG) indices for monitoring the depth of anesthesia have not been adjusted for age. This study aims to identify the most suitable EEG indices for monitoring anesthesia depth across different age groups. Method In here, we conducted a prospective observational trial to observe whether different EEG features in different age groups can detect anesthesia depth and compare their performance. Results In Group 1, absolute θ had the highest prediction probability (Pk) value (0.78 ± 0.07), while relative γ had the lowest relative coefficient of variation (CV) value in states 1 (0.160), 2 (0.153), 3 (0.214), and 4 (0.144). In Group 2, absolute θ had the highest Pk value (0.81 ± 0.09), and relative γ had the lowest CV value in states 1 (0.159), 2 (0.178), 3 (0.140), and 4 (0.095). In Group 3, absolute δ had the highest Pk value (0.79 ± 0.08), with absolute slow wave having the lowest CV value in states 1 (0.196), 2 (0.258), 3 (0.295), and 4 (0.181). In Group 4, absolute δ had the highest Pk value (0.75 ± 0.10), and absolute slow wave had the lowest CV value in states 1 (0.176), 2 (0.192), 3 (0.185), and 4 (0.144). Conclusions In this study, we found that absolute θ and relative γ are the most suitable choices for young and middle-aged patients, while absolute δ and absolute slow wave are the most suitable choices for young elderly and elderly patients.

EQ-5D-5L value set for Norway: a hybrid model using cTTO and DCE data.

To develop the Norwegian value set for the EQ-5D-5L based on interviews with a representative sample of the Norwegian adult population. Random and quota sampling were used to recruit the sample of adults (age> 18 years) representative of the Norwegian general population. Data collection followed EQ-VT 2.1 undertaken before and after the COVID-19 pandemic from November 2019 to December 2022, using PC-assisted and video conferencing interviews, respectively. Each respondent valued 10 health states using composite time trade-off (cTTO) and 7 health states using a discrete choice experiment (DCE).Different statistical models were assessed for logical consistency and predictive accuracy using cTTO and DCE data alone or in combination as hybrid models. Of the 1,321 respondents, 1,237 met inclusion criteria. All statistical models demonstrated logical consistency. The weighted hybrid model combining both cTTOand DCE data was preferred and had the highest predictive accuracy. Predicted values ranged from -0.453 to 1, and the dimension of anxiety/depression was the most highly valued by respondents, followed by pain/discomfort, self-care, mobility, and usual activities. These findings are not dissimilar to those for most Western European countries, and regression coefficients are closest to those for other Scandinavian countries. This study provides the Norwegian value set for the EQ-5D-5L based on health state values obtained from members of the adult general population in Norway.This is an important contribution to economic evaluation and the broader application ofthe EQ-5D-5L in Norway including clinical and health services research, and quality measurement.

Musings on SVD and pseudo entanglement entropies

Pseudo-entropy and SVD entropy are generalizations of the entanglement entropy that involve post-selection. In this work we analyze their properties as measures on the spaces of quantum states and argue that their excess provides useful characterization of a difference between two (i.e. pre-selected and post-selected) states, which shares certain features and in certain cases can be identified as a metric. In particular, when applied to link complement states that are associated to topological links via Chern-Simons theory, these generalized entropies and their excess provide a novel quantification of a difference between corresponding links. We discuss the dependence of such entropy measures on the level of Chern-Simons theory and determine their asymptotic values for certain link states. We find that imaginary part of the pseudo-entropy is sensitive to, and can diagnose chirality of knots. We also consider properties of entropy measures for simpler quantum mechanical systems, such as generalized SU(2) and SU(1,1) coherent states, and tripartite GHZ and W states.

GDT: Multi-agent reinforcement learning framework based on adaptive grouping dynamic topological space

In many real-world scenarios, tasks involve coordinating multiple agents, such as managing robot clusters, drone swarms, and autonomous vehicles. These tasks are commonly addressed using Multi-Agent Reinforcement Learning (MARL). However, existing MARL algorithms often lack foresight regarding the number and types of agents involved, requiring agents to generalize across various task configurations. This may lead to suboptimal performance due to underestimated action values and the selection of less effective joint policies. To address these challenges, we propose a novel multi-agent deep reinforcement learning framework, called multi-agent reinforcement learning framework based on adaptive grouping dynamic topological space (GDT). GDT utilizes a group mesh topology to interconnect the local action value functions of each agent, enabling effective coordination and knowledge sharing among agents. By computing three different interpretations of action value functions, GDT overcomes monotonicity constraints and derives more effective overall action value functions. Additionally, GDT groups agents with high similarity to facilitate parameter sharing, thereby enhancing knowledge transfer and generalization across different scenarios. Furthermore, GDT introduces a strategy regularization method for optimal exploration of multiple action spaces. This method assigns each agent an independent entropy temperature during exploration, enabling agents to efficiently explore potential actions and approximate total state values. Experimental results demonstrate that our approach, termed GDT, significantly outperforms state-of-the-art algorithms on Google Research Football (GRF) and the StarCraft Multi-Agent Challenge (SMAC). Particularly in SMAC tasks, GDT achieves a success rate of nearly 100% across almost all Hard Map and Super Hard Map scenarios. Additionally, we validate the effectiveness of our algorithm on Non-monotonic Matrix Games.

Characterizing non-Markovian and coherent errors in quantum simulation

Quantum simulation of many-body systems, particularly using ultracold atoms and trapped ions, presents a unique form of quantum control—it is a direct implementation of a multi-qubit gate generated by the Hamiltonian. As a consequence, it also faces a unique challenge in terms of benchmarking, because the well-established gate benchmarking techniques are unsuitable for this form of quantum control. Here we show that the symmetries of the target many-body Hamiltonian can be used not only to benchmark but to characterize experimental errors in the quantum simulation. We use our results to develop protocols to characterize these errors, which can be implemented using state-of-the-art technology. We consider two forms of errors: (i) unitary errors arising out of systematic errors in the applied Hamiltonian and (ii) canonical non-Markovian errors arising out of random shot-to-shot fluctuations in the applied Hamiltonian. We show that the dynamics of the expectation value of the target Hamiltonian itself, which is ideally constant in time, can be used to characterize these errors. In the presence of errors, the expectation value of the target Hamiltonian shows a characteristic thermalization dynamics, when it satisfies the operator thermalization hypothesis (OTH). That is, an oscillation in the short time followed by relaxation to a steady-state value in the long time limit. We show that while the steady-state value can be used to characterize the coherent errors, the amplitude of the oscillations can be used to estimate the non-Markovian errors. We prove a sandwich theorem to establish a linear relation between the amplitude of the oscillations and the magnitude of the non-Markovian errors. Moreover, by varying the initial state, we show that the steady state values can be used to completely construct the generator of the coherent errors. Using these results, we develop two experimental protocols to characterize the unitary errors based on these results, one of which requires single-qubit addressing and the other one doesn't. We also develop a protocol to characterize non-Markovian errors. Published by the American Physical Society 2024

An algorithm that excavates suboptimal states and improves Q-learning

Abstract Reinforcement learning is inspired by the trial-and-error method in animal learning, where the reward values obtained from the interaction of the agent with the environment are used as feedback signals to train the agent. Reinforcement learning has attracted extensive attention in recent years. It is mainly used to solve sequential decision-making problems and has been applied to various aspects of life, such as autonomous driving, game gaming, and robotics. Exploration and exploitation are the main characteristics that distinguish reinforcement learning methods from other learning methods. Reinforcement learning methods need reward optimization algorithms to better balance exploration and exploitation. Aiming at the problems of unbalanced exploration and a large number of repeated explorations in the Q-learning algorithm in the MDP environment, an algorithm that excavates suboptimal states and improves Q-learning was proposed. It adopts the exploration idea of ‘exploring the potential of the second-best’, and explores the state with suboptimal state value, and calculates the exploration probability value according to the distance between the current state and the goal state. The larger the distance, the higher the exploration demand of the agent. In addition, only the immediate reward and the maximum action value of the next state are needed to calculate the Q value. Through the simulation experiments in two different MDP environments, The frozenLake8x8 environment and the CliffWalking environment, the results verify that the proposed algorithm obtains the highest average cumulative reward and the least total time consumption.

Delineating anticipatory arousal from reward consumption: evaluating fixed-intervals in cocaine seeking-taking response chains.

Anticipation is a critical antecedent to drug use, in which the prospect of imminent drug availability can potently motivate instrumental actions directed to procure it. Models that capture the behavioral dynamics that precede drug access may allow for the dissociation of key neural mechanisms underlying appetitive or consummatory processes in drug self-administration. We aimed to isolate measurements attributed to the procurement and consumption of a reward by defining distinct actions for each using a chain-schedule of reinforcement. Male Long-Evans rats were trained to self-administer cocaine or saccharin under a chained schedule of reinforcement (FI-FR) in order to dissociate appetitive ('seeking') from consummatory ('taking') behaviors. Completion of a fixed-interval (5min) was followed by 5min of continuously reinforced responding (FR1) on another lever. The FI-FR chain procedure appears to provide sensitive and dissociable dimensions of cocaine self-administration within a single experimental session. Importantly, we demonstrate that responding during the FI (i.e., seeking) link tracks with the incentive value of anticipated reward access - whereby response rates corresponded to expected reward magnitude, degree of reward-specific satiety, and general motivational state. The FI component is a sensitive and reliable index of motivational changes induced by either the extrinsic incentive value of reinforcement (i.e., anticipated dose) or intrinsic motive states (i.e., satiety or deprivation). This procedure provides a valuable tool for interrogating the neural dynamics of drug-seeking and -taking behavior, in isolation.

Adaptive Multi-layer Attention Double Dueling Deep Q-Network for Muti-agent Reinforcement Learning

Abstract. In multi-agent fields, traditional muti-agent DQN methods often suffer from overestimation bias and overestimation of unimportant actions, especially when state-action Q-value differences are slight. To deal with such issue, we present an adaptive Multi-layer Attention Double Dueling Deep Q-Network (MAD-D3QN) model, aiming to improve decision-making accuracy in complex multi-agent environments. The proposed model utilizes two attention layers that dynamically calculate state value and action advantage weights, facilitating more precise Q-value estimation and reducing the common overestimation bias. Related experiments carried out in StarWar II scenarios show that the MAD-D3QN model obviously outperforms traditional methods (IQL,DQN), achieving higher decision efficiency and robustness. Our findings demonstrates that the MAD-D3QN framework not only promotes the state-of-the-art in multi-agent reinforcement learning but also provides potential applications in real-world cooperative tasks. Future research will delve into the integration of advanced multi-agent communication structures to further enhance model adaptability.

Modified Shooting with Discretization Validation for Non-Standard Optimal Control Problem: Case Study for Four-Stage Royalty Payment Problem

A modified shooting method augmented by discretization validation is presented in this paper to address the challenges inherent in non-standard optimal control problems. Specifically, a specific case study involving four-stage royalty payment functions is focused on, with the aim of effectively optimizing these complex, non-differentiable functions. The shooting method is adapted and enhanced to compute optimal solutions, and its accuracy is rigorously confirmed through discretization techniques. The primary objectives involve maximizing the performance index and determining optimal control strategies for scenarios where the final state variable remains unknown. In this study, the royalty payment is defined as a four-stage piecewise function. The incorporation of piecewise royalty functions introduces non-differentiability at specific time intervals, necessitating innovative approaches for finding optimal solutions. This, in turn, leads to the utilization of the continuous hyperbolic tangent (tanh) function to address the non-differentiability issue. A hybrid shooting method, combining the Newton and Golden Section Search methods, is employed in the C++ programming language to compute the unknown final state value. A new natural boundary condition, based on established theory, is introduced to further facilitate the investigation. Discretization methods such as Euler, Runge-Kutta, Trapezoidal, and Hermite-Simpson approximations are employed for validation. The validation process entails the use of the AMPL programming language with the MINOS solver. Comparative analyses reveal that the modified shooting method yields more accurate optimal results than discretization methods, thus demonstrating the method’s effectiveness in addressing non-standard optimal control problems. The significance of fundamental theories in addressing real-world challenges is underscored by this research, providing valuable insights for future researchers exploring mathematical approaches in similar contexts. The study contributes to the continued relevance of the academic field, particularly in science and mathematics education.

Opto-mechanical Synthesis and Radiation protection of Environmentally friendly Nd2O3-doped Ba-Ga-Al-B Glasses

A new Ba-borate glass doped with Nd2O3 was synthesized based on the BaO-Ga2O3-Al2O3-B2O3 composition. Al2O3 is partially replaced by Nd2O3 with 0, 0.5, 1, and 2 (mol%) concentrations. Glass samples were manufactured via traditional melting methods and were characterized based on XRD reflections, Archimedes' density principle, UV-Vis spectrum, Makishima-Mackenzie’s principle, and the free Phy-X/PSD-soft programmed. The produced samples are visibly clear and transparent, with an amorphous nature. The measured density ranged from 3.31 to 3.49 g/cm3, while molar volume was decreased with Nd2O3/Al2O3 substitution. Additionally, the OPD values ranged from 65.366 to 65.789 g atom/l, and the V0 values ranged from 15.298 to 15.200 cc/mol, introducing an inverse relationship. The results indicated that adding neodymium instead of alumina results in a very slight decrease in all calculated elastic moduli and their related parameters. The optical band gap (Eg) value was decreased with the introduction of Nd2O3 while the index of refraction (n) and the width of localized state (EUr) values have been increased. This would be expected due to the Eg is inversely proportion to the n and EUr values. Furthermore, the refraction loss (RL) molar refraction (Rm), and molar polarizability have been estimated. The findings obtained provided useful information regarding the radiation-shielding properties of the glasses under investigation. Additionally, they provide strong support for contemporary ideas of glass's structure and properties, which help create novel glass materials and their uses in radiation shielding.

Transformer winding state diagnosis method based on short-circuit impulse response and multi-feature joint

Abstract To investigate the relationship between the physical characteristics of transformer short-circuit impulse signals and winding deformation, this paper proposes a transformer winding state diagnosis method based on the combination of short-circuit impulse response and multiple features. Firstly, based on the relative displacement model of a single degree of freedom system, a winding short-circuit impulse response spectrum is constructed, and the energy entropy characteristics of different frequency bands are extracted using the Hilbert energy spectrum. Secondly, the energy spectrum is converted into a time-frequency matrix, and its energy density distribution and short-term energy attenuation changes are quantified. Then, we perform support vector regression (SVD) decomposition and calculate the proportion of singular value vectors. Finally, multiple feature quantities are combined to construct a feature set, which is then input into the SVD model optimized by the particle swarm algorithm (PSO) for diagnosis. The experimental results show that the proposed method can accurately extract the physical characteristics of short-circuit impulse signals, and the error between the obtained transformer winding deformation diagnosis value and the actual state value is only 3.6%, which can provide guidance for online monitoring of the transformer winding state.

Distributed minimum error entropy with fiducial points Kalman filter for state tracking

With the growing size of the system, this distributed Kalman filter (DKF) is widely used in multi-sensor networks. However, it is difficult for DKF to accurately estimate state values in non-Gaussian noise environments. In this paper, a regression equation is first constructed to contain all sensor node information. Then, by bringing the minimum error entropy with fiducial points (MEEF) standard into the process of information fusion, a robust algorithm named centralized MEEF KF (CMEEF-KF) is presented, which is robust to non-Gaussian noise and unusual data. Furthermore, to overcome the communication burden of CMEEF-KF in sensor networks, the distributed MEEF-KF (DMEEF-KF) is developed, which construct a framework of consensus average method for node information fusion. Specifically, each sensor only exchanges the key information with its neighborhoods. In addition, in order to make the algorithm able to cope with the nonlinear state estimation problem, the distributed MEEF extended Kalman filter is also proposed. Eventually, the effectiveness of the suggested algorithms is demonstrated by land vehicle navigation and power system tracking state estimation using a 10-node sensor network.

TREND OF CASSAVA YIELD/PRODCUTION IN IN KOGI EAST SENATORIAL DISTRICT, KOGI STATE, NIGERIA

This study examined the trends in cassava yield and production in the Kogi East Senatorial District of Kogi State, Nigeria, focusing on the perceptions of local farmers regarding yield changes over the past five years and the factors influencing these trends. A total of 403 respondents were surveyed, revealing that 71.3% of the farmers perceived an increase in cassava yields, while 28.7% reported stable yields. The primary factors contributing to the perceived increase included the use of improved cassava varieties (58.1%) and climate variability (41.9%). Furthermore, the statistical analysis indicated a stationary R-squared value of 0.792, suggesting a robust model fit for predicting future production trends. Forecasts indicated a steady increase in cassava production per hectare from 2024 to 2033, with projected yields rising from 17.33 tons per hectare in 2024 to 18.54 tons per hectare by 2033. Despite these positive trends, the study identified significant challenges posed by climate variability, with 76.7% of respondents recognizing a high impact on production. The findings underscore the urgent need for targeted interventions, including the promotion of climate-resilient cassava varieties, improved access to quality planting materials, and the implementation of sustainable agricultural practices. Overall, this study provides critical insights into the cassava production landscape in Kogi East and highlights the importance of collaborative efforts among stakeholders to enhance productivity and ensure food security in the region.

The hydromorphological quality of the basin of Mexico: A proposal of its indicator value of the ecological state in the riparian ecosystem

The characterization of hydromorphological quality is the evaluation of the physical structure and the flow regime associated with fluvial ecosystems. Its value indicates the state of ecosystem conservation, as well as the anthropogenic pressures that disturb it. The present study proposes an hydromorphological quality (HYQI) index that aims to establish reference conditions in the preserved rivers and springs in the Basin of Mexico, through: (i) the basin quality associated with the riparian zone’s state, including the vegetation’s naturalness, level of erosion, and land use in 13 sub-basins (63 sites); (ii) hydrology, related to natural or disturbance conditions in the channel; (iii) anthropogenic alterations in the riparian zone, and (iv) the characterization of the trophic level. The final evaluation is divided into five classes: high (> 100), good (76-99), moderate (51-75), bad (26-50), and poor (< 25). The HQYI evaluation showed that 44 sites have a high rating (120 to 100 points), where potential reference conditions for the Mexico Basin can be recognized. The remaining 19 sites have good to poor quality conditions. The vegetation cover was represented by 70% of native species in one of three types of forest: Pinus, Abies, and mixed forest dominated by Quercus. Modifications in the canal structure, extraction and retention of water, and introduced plant species were the causes that confirmed the moderate quality value in the middle and lower portions. The HQYI value was found to be significantly correlated with nutrient water enrichments with soluble reactive phosphorus and dissolved inorganic nitrogen. Therefore, this index is recommended for monitoring the Basin of Mexico and registering multiple environmental stressors.

Application of Discrete Variable-Gain-Based Self-Immunity Control to Flywheel Energy Storage Systems

For the study of the trade-off between steady-state error and transient response in control systems for flywheel energy storage, a controller with a discrete variable gain is proposed. This controller aims to adapt to changes in the system state by dynamically adjusting the controller gain to optimize the system’s anti-disturbance performance. Theoretical analysis and mathematical derivation demonstrate that increasing the observer gain can significantly enhance the system’s anti-disturbance capability. However, this increase also results in overshooting, which highlights the limitations of traditional control methods in achieving both system stability and anti-disturbance performance. A discrete variable-gain extended state observer is designed. The gain of this observer can be adaptively adjusted according to a system state value, enabling the effective control of both steady-state error and transient response. Additionally, the stability of the proposed control method was analyzed and verified, ensuring its effectiveness and reliability for practical applications. Finally, the effectiveness of the proposed method in improving system performance is demonstrated by simulation results.

Using linear and nonlinear entanglement witnesses to generate and detect bound entangled states on an IBM quantum processor

Abstract We investigate bound entanglement in three-qubit mixed states which are diagonal in the Greenberger-Horne-Zeilinger (GHZ) basis. Entanglement in these states is detected using entanglement witnesses and the analysis focuses on states exhibiting positive partial transpose (PPT). We then compare the detection capabilities of optimal linear and nonlinear entanglement witnesses. In theory, both linear and nonlinear witnesses produce non-negative values for separable states and negative values for some entangled GHZ diagonal states with PPT, indicating the presence of entanglement. Our experimental results reveal that in cases where linear entanglement witnesses fail to detect entanglement, nonlinear witnesses are consistently able to identify its presence. Optimal linear and nonlinear witnesses were generated on an IBM quantum computer and their performance was evaluated using two bound entangled states (Kay and Kye states) from the literature, and randomly generated entangled states in the GHZ diagonal form. Additionally, we propose a general quantum circuit for generating a three-qubit GHZ diagonal mixed state using a six-qubit pure state on the IBM quantum processor. We experimentally implemented the circuit to obtain expectation values for three-qubit mixed states and compute the corresponding entanglement witnesses.