Projective Measurements Research Articles

Quantifying Quantum Steering with Limited Resources: A Semi‐supervised Machine Learning Approach

AbstractQuantum steering, an intermediate quantum correlation lying between entanglement and nonlocality, has emerged as a critical quantum resource for a variety of quantum information processing tasks such as quantum key distribution and true randomness generation. The ability to detect and quantify quantum steering is crucial for these applications. Semi‐definite programming (SDP) has proven to be a valuable tool to quantify quantum steering. However, the challenge lies in the fact that the optimal measurement strategy is not priori known, making it time‐consuming to compute the steerable measure for any given quantum state. Furthermore, the utilization of SDP requires full information of the quantum state, necessitating quantum state tomography, which can be complex and resource‐consuming. In this work, the semi‐supervised self‐training model is used to estimate the steerable weight, a pivotal measure of quantum steering. The model can be trained using a limited amount of labeled data, thus reducing the time for labeling. The features are constructed by the probabilities derived by performing three sets of projective measurements under arbitrary local unitary transformations on the target states, circumventing the need for quantum tomography. The model demonstrates robust generalization capabilities and can achieve high levels of precision with limited resources.

Sharing tripartite nonlocality sequentially using only projective measurements

Sharing tripartite nonlocality sequentially using only projective measurements

A binary coding method for half-period sinusoidal stripes in focused projection

Abstract During sinusoidal streak projection measurements, the nonlinear responses inherent in projectors and cameras can significantly alter the characteristics of projection and imaging. Traditional techniques require precise out-of-focus levels to achieve accurate depth measurements, which inherently limit the depth range that can be effectively measured. Addressing this limitation, this paper introduces an innovative binarization coding method for half-period sinusoidal stripes in focused projection. Our approach begins with a binarization process that encodes the half-period sinusoidal stripes. We then capture these stripes as they are modulated by the height of the object under test. The subsequent synthesis of the half-period sinusoidal stripes is achieved through a method of superposition calculation. To enhance the experimental procedure, we employ a four-step phase-shifting technique, complemented by an assisted phase unfolding using the gray code method. For the validation of our method, a standard ball with a diameter of 50.8140 mm was measured. The results are compelling, demonstrating a root mean square error of merely 0.0285 mm. Comparative experimental results prove that the proposed method can effectively avoid the influence of nonlinearity, and also obtain high-precision reconstruction results for discontinuous scenes.

The effect of state preparation on the probe-bath parameters estimation

Abstract Projective measurement is a popular method of initial state preparation, which always prepares a pure state. However, in various physical situations of interest, this selective measurement becomes unrealistic. In this paper, we investigate the role of pulsed measurement (a unitary operation) on the estimation of system-environment parameters and compare the estimation results obtained via projective measurement with the results obtained via unitary operation. We argue that in typical situations, parameters can be estimated with higher accuracy if the initial state is prepared with the unitary operator (a pulse). We consider the spin-spin model in which a central two-level system (probe) interacts with a collection of two-level systems (bath). The probe interacts with the bath and attains thermal equilibrium. Then, via unitary operation, the initial state is prepared which evolves unitarily. The properties of the bath are imprinted on the reduced dynamics. Due to the initial probe-bath correlations present in the thermal equilibrium state, an additional factor arises in the dynamics, which has an important role in the parameter estimation. In this paper, we study the estimation of bath temperature and probe-bath coupling strength which is quantified by the quantum Fisher information. Our results are promising as one can improve the precision of the estimates by orders of magnitude (especially in the coupling strength case) via unitary operation and by incorporating the effect of initial correlations.

Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain

Understanding the influence of measurements on the properties of many-body systems is a fundamental problem in quantum mechanics and for quantum technologies. This paper explores how a finite density of stochastic local measurement modifies a given state’s entanglement structure. Considering various measurement protocols, we explore the typical quantum correlations of their associated projected ensembles arising from the ground state of the quantum Ising model. Using large-scale numerical simulations, we demonstrate substantial differences among inequivalent measurement protocols. Surprisingly, we observe that forced on-site measurements can enhance both bipartite and multipartite entanglement. We present a phenomenological toy model and perturbative calculations to analytically support these results. Furthermore, we extend these considerations to the non-Hermitian Ising model, naturally arising in optically monitored systems, and we show that its qualitative entanglement features are not altered by a finite density of projective measurements. Overall, these results reveal a complex phenomenology where local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.

The Role of Consumer Empowerment and Its Comparison in Financial Inclusion in the Global South

This research examines the role of consumer empowerment in advancing financial inclusion across the Global South, focusing on Africa, Latin America, and Asia. The study aims to understand how empowering consumers through economic literacy, protection, and equitable access facilitates meaningful participation in formal financial systems. It employs a qualitative analysis of case studies from Kenya, Bangladesh, Brazil, South Africa, Liberia and India, combined with a review of relevant policy frameworks and innovations in digital financial services. Findings reveal that consumer empowerment significantly enhances financial inclusion by building trust, fostering financial capability, and enabling access to tailored products. Case studies highlight the transformative impact of mobile platforms like M-Pesa and bKash, Liberia linking the informal financial sector to the formal financial sector pilot project and regulatory measures such as Brazil’s consumer protection laws and India’s responsible lending guidelines. However, barriers such as limited infrastructure, regulatory gaps, and socio-cultural norms continue to impede progress. The study concludes that bridging these gaps requires collaborative efforts to strengthen consumer protection, expand literacy programs, and leverage technology for equitable financial access. By addressing these challenges, stakeholders can create inclusive and resilient financial ecosystems that drive sustainable economic growth in the Global South.

Radiation from Dirac fermions caused by a projective measurement

Radiation from Dirac fermions caused by a projective measurement

Compton scattering from proton pairs – illustrating weak and strong measurements

Abstract Neutrons interacting with protons in Compton scattering is here chosen as an example of a non-trivial quantum measurement. It illustrates a situation where a probe particle makes an observation (a weak measurement) of the studied protons, preparing for a final state in which one of them takes up the recoil in the collision. The proton is ejected during a strong (projective) measurement that selects one particular momentum value out of the proton’s initial distribution of momentum states. This course of events in the measurement process is evidenced by the observation that destructive interference appears during the weak interaction stage which leads to a strongly reduced neutron cross section for the proton system.

Optimizing Cost Efficiency through Cost Control in Construction Projects: A Review

This study explores various methodologies and factors influencing budget performance across different sectors, particularly in construction and public budgeting. Construction projects are inherently complex and prone to cost overruns, making cost control a critical aspect of project management. This study investigates the impact of cost control on cost efficiency in construction projects. A neural network model was utilized to identify key management factors affecting project budget performance, focusing on critical aspects such as project manager experience, team turnover, and budget updates. Several monitoring techniques for cost and performance deviations, including Activity-Based Ratios, were also analyzed, revealing their varying effectiveness. In the public sector, performance-based budgeting systems were discussed, with an emphasis on integrating planning and performance metrics for more informed decision-making. Challenges in implementing such systems were highlighted, particularly regarding political and organizational barriers. In construction, various approaches were examined, including cost estimation frameworks and performance-based budgeting tools. The research underlined the importance of accurate budgeting and cost control measures in both construction projects and public administration, suggesting that strategic adjustments, better forecasting, and active stakeholder participation could improve overall budget performance. This research paper presents a comparative analysis of various process-based cost control models utilized in construction projects. The objective is to evaluate each model’s effectiveness, advantages, and limitations to provide insights for project managers in selecting the most suitable approach for their specific project needs. Key Words: Cost Efficiency, Cost Control, Construction, Projects

Ptychographic estimation of pure multiqubit states in a quantum device

Quantum ptychography is a method for estimating an unknown pure quantum state by subjecting it to overlapping projections, each one followed by a projective measurement on a single prescribed basis. Here, we present a comprehensive study of this method applied for estimating n-qubit states in a circuit-based quantum computer, including numerical simulations and experiments carried out on an IBM superconducting quantum processor. The intermediate projections are implemented through Pauli measurements on one qubit at a time, which sets the number of ptychographic circuits to 3n (in contrast to the 3n circuits for standard Pauli tomography); the final projective measurement in the computational basis is preceded by the quantum Fourier transform (QFT). Due to the large depth and number of two-qubit gates of the QFT circuit, which is unsuitable for noisy devices, we also test the approximate QFT (AQFT) and separable unitary operations. Using the QFT and AQFT of degree 2, we obtained high estimation fidelities in all tests with separable and entangled states for up to three and four qubits, respectively; on the other hand, the separable unitaries in this scenario provided good estimations only for separable states, in general. Our results compare favorably with recent results in the literature, and we discuss further alternatives to make the ptychographic method scalable for the current noisy devices.

The Existence of Distinguishable Bases in Three-Dimensional Subspaces of Qutrit-Qudit Systems Under One-Way Local Projective Measurements and Classical Communication

The Existence of Distinguishable Bases in Three-Dimensional Subspaces of Qutrit-Qudit Systems Under One-Way Local Projective Measurements and Classical Communication

Process tomography of structured optical gates with convolutional neural networks

Abstract Efficient and accurate characterization of an experimental setup is a critical requirement in any physical setting. In the quantum realm, the characterization of an unknown operator is experimentally accomplished via Quantum Process Tomography (QPT). This technique combines the outcomes of different projective measurements to reconstruct the underlying process matrix, typically extracted from maximum-likelihood estimation. Here, we exploit the logical correspondence between optical polarization and two-level quantum systems to retrieve the complex action of structured metasurfaces within a QPT-inspired context. In particular, we investigate a deep-learning approach that allows for fast and accurate reconstructions of space-dependent SU(2) operators by only processing a minimal set of measurements. We train a convolutional neural network based on a scalable U-Net architecture to process entire experimental images in parallel. Synthetic processes are reconstructed with average fidelity above 90%. The performance of our routine is experimentally validated in the case of space-dependent polarization transformations acting on a classical laser beam. Our approach further expands the toolbox of data-driven approaches to QPT and shows promise in the real-time characterization of complex optical gates.

Influence of large-diameter shield tunneling on deformation of adjacent high-speed railway subgrade in soft soils and effectiveness of protective measures

The excavation of large-diameter shield tunnels in soft soils inevitably impacts adjacent high-speed railway infrastructure. This study investigates the effects of constructing a 14.02 m large-diameter shield tunnel on the deformation of a nearby high-speed railway subgrade in soft soils of Shanghai, and evaluates the effectiveness of various protective measures. A numerical model was developed to simulate the horizontal deformations of railway subgrade piles, as well as the vertical and horizontal deformations of track slab resulting from shield excavation. Comprehensive real-time monitoring of track slab displacements in both vertical and horizontal directions, along with ground surface deformation, was conducted. The accuracy of the computational model and the effectiveness of the implemented protective measures were validated through field measurements. The results demonstrate that isolation piles with coupling beams proved to be the most effective method for protecting the railway subgrade. The maximum observed ground settlement above the tunnel reached −20.3 mm, while the peak heave was recorded at 3.7 mm. Notably, the additional vertical and horizontal deformations of the high-speed railway track were successfully constrained within the 2-mm threshold. These findings provide valuable insights for safety assessments and the implementation of protective measures in similar projects.

Entropic partial orderings of quantum measurements

Abstract We investigate four partial orderings on the space of quantum measurements (i.e. on POVMs or positive operator valued measures), describing four notions of coarse/fine-ness of measurement. These are the partial orderings induced by: (1) classical post-processing, (2) measured relative entropy, (3) observational entropy, and (4) linear relation of POVMs. The orderings form a hierarchy of implication, where e.g. post-processing relation implies all the others. We show that this hierarchy is strict for general POVMs, with examples showing that all four orderings are strictly inequivalent. Restricted to projective measurements, all are equivalent. Finally we show that observational entropy equality $S_M = S_N$ (for all $\rho$) holds if and only if POVMs $M \equiv N$ are post-processing equivalent, which shows that the first three orderings induce identical equivalence classes.

Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools. Published by the American Physical Society 2024

SecoInfer: Secure DNN End-Edge Collaborative Inference Framework Optimizing Privacy and Latency

End-edge collaborative inference enhances computational efficiency by segmenting a deep neural network (DNN) model into two parts, executed across the end device and the edge node. However, existing collaborative inference strategies often involve transmitting original inputs from the end device to the edge node, resulting in significant risks of user detail leakage without requiring input reconstruction. Therefore, in this work, we present SecoInfer, a secure layer-level DNN end-edge collaborative inference framework. SecoInfer achieves joint optimization of data privacy and inference latency for DNN partition solutions that meet latency constraints, supported by three key designs. First, the privacy-aware DNN layer projection measurement quantifies the difficulty adversaries encounter in reconstructing the original input from the intermediate output of each layer. Then, the latency-privacy integrated structure modeling enables the direct calculation of the privacy measurement and inference latency for each partition solution from a list element or a directed acyclic graph (DAG) cut. Finally, the two-stage latency constraint adjustment scheme narrows down the search space of feasible partition solutions at the block level and fine-tunes the final one to meet the latency constraint based on layer depth. We prototype SecoInfer, utilizing a Raspberry Pi 4B as the end device and a server with an NVIDIA GeForce RTX 3060 GPU as the edge node. Experimental results demonstrate that under latency constraints of 20 ms, 33 ms, and 40 ms, SecoInfer reduces adversarial data reconstruction by 9.84%, 19.26%, and 25.18%, respectively, without any loss of task model accuracy. SecoInfer also enhances efficiency, reducing the time needed to determine optimal end-edge partition solutions on a Raspberry Pi 4B by 18.04%.

Optimizing neurosurgery clinic operations: a comparative study of interventions in Finland's public healthcare system.

The Finnish public healthcare system aims to ensure equal access to health services for all but faces challenges in meeting the demand for specialized care, such as neurosurgery, due to resource constraints. This study investigates interventions to increase resources at a neurosurgery outpatient clinic to improve patient care without compromising waiting times for diagnoses and treatments, leveraging Finland's unique healthcare landscape. The study was conducted at Kuopio University Hospital's Department of Neurosurgery, the sole provider of neurosurgical care in Eastern Finland. Two interventions were designed to optimize clinic operations: one focusing on dynamic resource allocation through continuous monitoring and the other on establishing a fixed additional neurosurgeon slot. Process capability and regression analysis were employed to evaluate the effects of these interventions on the number of outpatient visits and the variability in daily patient numbers. The preliminary analysis showed an average of 9.3 outpatient visits per day (SD 5.2). The introduction of an additional neurosurgeon led to an increase of 5.014 visits per day, according to the regression analysis performed before the interventions. Following the interventions, the clinic observed an increase in the average number of daily outpatient visits to 9.8 after the first intervention and 11.6 after the second, with corresponding improvements in the number of neurosurgeons present. The second intervention, which established a predictable additional resource, resulted in a more significant improvement in process efficiency and stability. After the interventions, the number of new neurosurgical first patient visits increased by 7% (97 patients). This study demonstrates the importance of structured and predictable resource allocation in enhancing the efficiency of specialized healthcare services, particularly in neurosurgery. It also underscores the potential of planned interventions to manage and improve patient care in a publicly funded healthcare system, despite the challenges posed by limited resources and the need for prioritization. Moreover, the findings highlight the necessity of ongoing measurement and analysis of development projects to ensure sustained improvement and avoid regression in process quality.

Speed excess and total acceleration: a kinematical approach to entanglement

Abstract The total variance of a spin state is defined as the average of the variances of spin projection measurements along three orthogonal axes. We show that this quantity also gives the squared rotational speed of the state in projective space, averaged over all rotation axes. We compute the addition law, under system composition, for this quantity and find that, in the case of separable states, it is of simple pythagorean form. In the presence of entanglement, we find that the composite state ‘rotates faster than its parts’, thus unveiling a kinematical origin for the correlation of total variance with entanglement. We analyze a similar definition for the acceleration of a state under rotations, for both pure and mixed states, and probe numerically its relation with a wide array of entanglement related measures.

Qualitative study on sustainability of intervention measures in the Shandong Provincial Department's Joint Salt Reduction Project

Objective: To employ qualitative research methods to evaluate the sustainability of the Shandong-Ministry of Health Action on Salt and Hypertension (SMASH) interventions and their influencing factors. Method: In September 2023, interviewees meeting the inclusion criteria were recruited through purposive sampling in Jinan, Shandong Province. A semi-structured interview guide was designed based on the CFIR and RE-AIM frameworks. Personal in-depth interviews and focus group discussions were conducted to gather insights on the feasibility, effectiveness, and sustainability of the project interventions from various stakeholders, including representatives from the government, food manufacturers, restaurants, academia, and residents. Results: A total of 15 individuals participated in in-depth interviews, involving six representatives from food manufacturers, four from restaurants, three from the government, and two from academia. There were four focus group discussions with 30 residents. The study found that at the individual resident level, health awareness and the availability of sodium reduction tools in the market could affect their salt reduction practices. For food manufacturers and restaurants, consumers' preferences, technical challenges in reformulation, and government support were key factors determining the smooth progress of their salt reduction efforts. At the governmental level, multi-sectional coordination, chronic disease management demonstration areas, and the impact of the pandemic were the main factors influencing the implementation of sodium reduction interventions. Conclusion: Future endeavours should strengthen long-term management and optimise the complex influencing factors associated with intervention measures. This will be essential in sustaining and expanding the positive health outcomes achieved through the Shandong population sodium reduction strategy.

Cost Impact Factors and Control Measures of Road and Bridge Projects Based on Linear Regression Model

Cost Impact Factors and Control Measures of Road and Bridge Projects Based on Linear Regression Model