Projective Measurements Research Articles

All real projective measurements can be self-tested

Entangled quantum systems feature non-local correlations that are stronger than could be realized classically. This property makes it possible to perform self-testing, the strongest form of quantum functionality verification, which allows a classical user to deduce the quantum state and measurements used to produce a given set of measurement statistics. While self-testing of quantum states is well understood, self-testing of measurements, especially in high dimensions, remains relatively unexplored. Here we prove that every real projective measurement can be self-tested. Our approach employs the idea that existing self-tests can be extended to verify additional untrusted measurements, known as post-hoc self-testing. We formalize the method of post-hoc self-testing and establish the condition under which it can be applied. Using this condition, we construct self-tests for all real projective measurements. We build on this result to develop an iterative self-testing technique that provides a clear methodology for constructing new self-tests from pre-existing ones.

EPR steering paradox ‘2 Q = (2−δ) C ’

Einstein-Podolsky-Rosen (EPR) steering is a quantum nonlocality between entanglement and Bell’s nonlocality emphasizing the incompatibility of the local-hidden-state (LHS) model with quantum theory. It is well established that the EPR steering paradox is an essential method for determining steering, which reveals the nature of steering by logical contradiction. However, previous studies on the EPR steering paradox have only examined cases where the conditional states of the steered party are pure. In this work, we present the EPR steering paradox about the case when the conditional states of the steered party are mixed, which can be expressed as a paradoxical equality ‘ 2Q=2−δC ’ 0<δ<1 given by quantum (Q) and classical (C) theories. For any N-qubit state, in the two-setting steering protocol, the contradiction ‘ 2Q=2−δC ’ can be obtained if and only if a particular set of projective measurements of the steering party makes all the conditional states of the steered party pure, which also implies that the N-qubit state is steerable. Moreover, considering the conditional states of the steered party as mixed states, we are able to identify the full range of steerable states detectable through the EPR steering paradox method. This also means that, so far, one has found all the steerable states that can be recognized by the EPR steering paradox, which is significant for some typical quantum schemes such as quantum teleportation and quantum key distribution.

High-Photon-Loss Threshold Quantum Computing Using GHZ-State Measurements.

We propose fault-tolerant architectures based on performing projective measurements in the Greenberger-Horne-Zeilinger (GHZ) basis on constant-sized, entangled resource states. We present linear-optical constructions of the architectures, where the GHZ-state measurements are encoded to suppress the errors induced by photon loss and the probabilistic nature of linear optics. Simulations of our constructions demonstrate high single-photon-loss thresholds compared to the state-of-the-art linear-optical architecture realized with encoded two-qubit fusion measurements performed on constant-sized resource states. We believe this result shows a resource-efficient path to achieving photonic fault-tolerant quantum computing.

Assessing Spatial–Temporal Characteristics of Land Desertification from 1990 to 2020 in the Heihe River Basin Using Landsat Series Imagery

Monitoring the status and dynamics of desertification is one of the most important parts of combating it. In this study, 30 m high-resolution information on land desertification and restoration in the Heihe River basin (HRB) was extracted from the land cover database. The results indicate that land desertification coexists with land restoration in the HRB. In different periods, the area of land restoration was much larger than the area of land desertification in the HRB, and the HRB has undergone land restoration. Upstream of the HRB, there is a continuing trend of increasing land desertification associated with overgrazing in a context where climate change favors desertification reversal. In the middle and lower reaches, although climate variability and human activities favor land desertification, land desertification is still being reversed, and land restoration dominates. Implementing the eco-environmental protection project and desertification control measures, especially the Ecological Water Distribution Project (EWDP), contributes to the reversal of desertification in the middle and lower reaches of the HRB. However, the EWDP has indirectly led to the lowering of the water table in the middle reaches, resulting in local vegetation degradation. Therefore, there is an urgent need to transform the economic structure of the middle reaches to cope with water scarcity and land desertification.

Engineering quantum states from a spatially structured quantum eraser.

Quantum interference is a central resource in many quantum-enhanced tasks, from computation to communication. While usually occurring between identical photons, it can also be enabled by performing projective measurements that render the photons indistinguishable, a process known as quantum erasing. Structured light forms another hallmark of photonics, achieved by manipulating the degrees of freedom of light, and enables a multitude of applications in both classical and quantum regimes. By combining these ideas, we design and experimentally demonstrate a simple and robust scheme that tailors quantum interference to engineer photonic states with spatially structured coalescence along the transverse profile, a type of quantum mode with no classical counterpart. To achieve this, we locally tune the distinguishability of a photon pair by spatially structuring the polarization and creating a structured quantum eraser. We believe that these spatially engineered multiphoton quantum states may be of significance in fields such as quantum metrology, microscopy, and communication.

Growing Schrödinger's cat states by local unitary time evolution of product states

We envisage many-body systems described by quantum spin-chain Hamiltonians featuring a trivial separable eigenstate. For generic Hamiltonians, such a state represents a quantum scar. We show that, typically, a macroscopically entangled state naturally grows after a single projective measurement of just one spin in the quantum scar. Moreover, we identify a condition under which what is growing is a “Schrödinger's cat state.” Our analysis does not reveal any particular requirement for the entangled state to develop, provided that the quantum scar does not minimize/maximize a local conservation law. We study two explicit examples: systems described by generic Hamiltonians where spins interact in pairs, and models that exhibit a U(1) hidden symmetry. The latter can be reinterpreted as a two-leg ladder in which the interactions along the legs are controlled by the local state on the other leg through transistorlike building blocks. Published by the American Physical Society 2024

High-Fidelity, Multiqubit Generalized Measurements with Dynamic Circuits

Generalized measurements, also called positive operator-valued measures (POVMs), can offer advantages over projective measurements in various quantum information tasks. Here, we realize a generalized measurement of one and two superconducting qubits with high fidelity and in a single experimental setting. To do so, we propose a hybrid method, the “Naimark-terminated binary tree,” based on a hybridization of Naimark’s dilation and binary tree techniques that leverages emerging hardware capabilities for midcircuit measurements and feed-forward control. Furthermore, we showcase a highly effective use of approximate compiling to enhance POVM fidelity in noisy conditions. We argue that our hybrid method scales better toward larger system sizes than its constituent methods and demonstrate its advantage by performing detector tomography of symmetric, informationally complete POVM (SIC POVM). Detector fidelity is further improved through a composite error-mitigation strategy that incorporates twirling and a newly devised conditional readout error mitigation. Looking forward, we expect improvements in approximate compilation and hardware noise for dynamic circuits to enable generalized measurements of larger multiqubit POVMs on superconducting qubits. Published by the American Physical Society 2024

Quantum information recovery from a black hole with a projective measurement

Quantum information recovery from a black hole with a projective measurement

Action formalism for geometric phases from self-closing quantum trajectories

When subject to measurements, quantum systems evolve along stochastic quantum trajectories that can be naturally equipped with a geometric phase observable via a post-selection in a final projective measurement. When post-selecting the trajectories to form a close loop, the geometric phase undergoes a topological transition driven by the measurement strength. Here, we study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system. We utilize a stochastic path integral that enables the analysis of rare self-closing events using action methods and develop the formalism to incorporate the measurement-induced geometric phase therein. We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter. Moreover, the inclusion of Gaussian corrections in the vicinity of the most probable self-closing trajectory quantitatively changes the transition point in agreement with results from numerical simulations of the full set of quantum trajectories.

Digital Measures Development: Lessons Learned from an Expert Workshop Addressing Cross-Therapeutic Area Measures of Sleep

Introduction: The Digital Measures Development: Core Measures of Sleep project, led by the Digital Medicine Society (DiMe), emphasizes the importance of sleep as a cornerstone of health and the need for standardized measurements of sleep and its disturbances outside the laboratory. This initiative recognizes the complex relationship between sleep and overall health, addressing it as both a symptom of underlying conditions and a consequence of therapeutic interventions. It aims to fill a crucial gap in healthcare by promoting the development of accessible, nonintrusive, and cost-effective digital tools for sleep assessment, focusing on factors important to patients, caregivers, and clinicians. Methods: A central feature of this project was an expert workshop conducted on April 19th, 2023. The workshop convened stakeholders from diverse backgrounds, including regulatory, payer, industry, academic, and patient groups, to deliberate on the project’s direction. This gathering focused on discussing the challenges and necessities of measuring sleep across various therapeutic areas, aiming to identify broad areas for initial focus while considering the feasibility of generalizing these measures where applicable. The methodological emphasis was on leveraging expert consensus to guide the project’s approach to digital sleep measurement. Results: The workshop resulted in the identification of seven key themes that will direct the DiMe Core Digital Measures of Sleep project and the broader field of sleep research moving forward. These themes underscore the project’s innovative approach to sleep health, highlighting the complexity of omni-therapeutic sleep measurement and identifying potential areas for targeted research and development. The discussions and outcomes of the workshop serve as a roadmap for enhancing digital sleep measurement tools, ensuring they are relevant, accurate, and capable of addressing the nuanced needs of diverse patient populations. Conclusion: The Digital Medicine Society’s Core Measures of Sleep project represents a pivotal effort to advance sleep health through digital innovation. By focusing on the development of standardized, patient-centric, and clinically relevant digital sleep assessment tools, the project addresses a significant need in healthcare. The expert workshop’s outcomes underscore the importance of collaborative, multi-stakeholder engagement in identifying and overcoming the challenges of sleep measurement. This initiative sets a new precedent for the integration of digital tools into sleep health research and practice, promising to improve outcomes for patients worldwide by enhancing our understanding and measurement of sleep.

Relative Entropy of Coherence Quantifies Performance in Bayesian Metrology

The ability of quantum states to be in superposition is one of the key features that sets them apart from the classical world. This “coherence” is rigorously quantified by resource theories, which aim to understand how such properties may be exploited in quantum technologies. There has been much research on what the resource theory of coherence can reveal about quantum metrology, almost all of which has been from the viewpoint of Fisher information. We prove, however, that the relative entropy of coherence, and its recent generalization to positive operator-valued measures (POVMs), naturally quantify the performance of Bayesian metrology. In particular, we show how a coherence measure can be applied to an ensemble of states. We then prove that during parameter estimation, the ensemble relative entropy of coherence (C) is equal to the difference between the optimal Holevo information (X), and the mutual information attained by a measurement (I). We call this relation the CXI equality. The ensemble coherence lets us visualize how much information is locked away in superposition and hence is inaccessible with a given measurement scheme and quantifies the advantage that would be gained by using a joint measurement on multiple states. Our results hold regardless of how the parameter is encoded in the state, encompassing unitary, dissipative, and discrete settings. We consider both projective measurements and general POVMs. This work suggests new directions for research in coherence, provides a novel operation interpretation for the relative entropy of coherence and its POVM generalization, and introduces a new tool to study the role of quantum features in metrology. Published by the American Physical Society 2024

Innovative BIM technology application in the construction management of highway

Within the global architecture, engineering, and construction industry, the use of Building Information Modeling (BIM) technology has significantly expanded. However, given the unique characteristics of road infrastructure, the application of BIM technology is still being explored. This article focuses on the Yuanchen Expressway, exploring innovative applications of BIM technology in comprehensive construction management. The project employs advanced technologies, including BIM, Geographic Information Systems (GIS), and the Internet of Things (IoT), to precisely identify critical nodes and breakthroughs. Supported by a detailed BIM model and a multi-level, diversified digital management platform, the project effectively addresses construction challenges in multiple tunnels, bridges, and complex interchanges, achieving intelligent construction innovation throughout the Yuanchen Expressway with BIM technology. By guiding construction through BIM models, utilizing a BIM+GIS-based management cloud platform system, and employing VR safety briefings, the project effectively reduces the difficulty of communication and coordination in project management, shortens the project measurement cycle, improves on-site work efficiency, and ensures comprehensive control and safety management. This article provides an exemplary case for the application of full-line construction management using BIM technology in the highway sector both in China and globally, offering new perspectives and strategies for highway construction management.

Editorial Vol.16(1)

It is with great pleasure that we present to you Volume 16, Number 1, 2024, of "Voice: Biannual and Bilingual Journal” published by Autar Dei Chaudharain Research Centre (ADCRC) at Mahendra Multiple Campus, Nepalgunj, Banke, Nepal. Our journal continues to uphold its primary aim of facilitating the exchange of expertise among scholars on a global scale, fostering a dynamic platform for intellectual discourse across various disciplines. In this edition, we proudly present a multidisciplinary collection of 13 articles, with eight contributions in English and five in Nepali. This diversity reflects our commitment to linguistic inclusivity and our effort to bridge scholarly communities across different languages.The range of topics covered in this issue underscores the breadth and depth of academic inquiry being pursued by our contributors. Highlights include an in-depth analysis of the socio-economic impacts of policy changes in Nepal during the crucial decade of the 1990s, examining realism and societal dynamics in selected novels of Shashi Deshpande, and a stability evaluation of the Lanedada Twin Tunnel in KTFT, focusing on the structural stability and safety measures of a significant infrastructural project. Additionally, we have an exploration of alcohol use and its socio-economic and health effects in the Tharu community of Raptisonari Rural Municipality. There is also an analysis of historical and literary perspectives on trauma and displacement in Khushwant Singh's "Train to Pakistan." An exploratory study on how economic changes affect consumer behavior in the jewelry market of Nepalgunj adds a practical economic perspective. A comparative study on the reading comprehension abilities of Tharu and non-Tharu students’ sheds light on educational performance influenced by cultural and linguistic factors. Finally, a contemporary assessment of Nepal’s food sovereignty status and related policies offers valuable insights into current agricultural and food security challenges.For our Nepali readers, we offer a detailed exploration of classical Sanskrit poetics and theories of rasa, along with an analysis of the purpose and cultural significance of traditional songs in the Ribdikot area. There is a historical overview and critical examination of trends in Nepali short stories, a comprehensive look at the fifth part of the Vedapurana's gems, and an analysis of the ideologies presented in the novel "Basai."

Interconversion between block coherence and multipartite entanglement in many-body systems

Coherence is intrinsically related to projective measurement. When the fixed projective measurement involves higher-rank projectors, the coherence resource is referred to as block coherence, which comes from the superposition of orthogonal subspaces. Here, we establish a set of quantitative relations for the interconversion between block coherence and multipartite entanglement under the framework of the block-incoherent operations. It is found that the converted multipartite entanglement is upper bounded by the initial block coherence of single-party system. Moreover, the generated multipartite entanglement can be transferred to its subsystems and restored to block coherence of the initial single-party system by means of local block-incoherent operations and classical communication. In addition, when only the coarse-grained quantum operations are accessible for the ancillary subsystems, we further demonstrate that a lossless resource interconversion is still realizable, and give a concrete example in three four-level systems. Our results provide a versatile approach to utilize different quantum resources in a cyclic fashion.

Sharing quantum steering via standard projective measurements

Sharing quantum steering via standard projective measurements

Projection-driven optimization framework for risk assessment of “dual carbon” audit in power grid enterprises with q-rung orthopair fuzzy MAGDM

Power grid enterprises are the backbone of promoting clean and low-carbon energy transformation, playing an important role in achieving carbon peak and carbon neutrality. It is very necessary to audit the implementation of the “dual carbon” work of power grid enterprises, in order to better implement the national “dual carbon” policy and serve the development of the national economy. The risk assessment of “dual carbon” audit in power grid enterprises is multiple-attribute group decision-making (MAGDM). In this study, in light with projection measure technique and bidirectional projection measure technique, four forms of projection measure technique with q-rung orthopair fuzzy sets (q-ROFSs) are conducted. Then, two weighed projection techniques are conducted to manage the MAGDM. Finally, a numerical example for risk assessment of “dual carbon” audit in power grid enterprises and comparative analysis is utilized to verify the developed techniques. The major contribution of this research is constructed: (1) entropy technique is implemented to determine the weight values in line with score number (SN) and accuracy number (AN); (2) two weighed projection techniques are implemented to put forward MAGDM with q-ROFSs; (3) the numerical example for risk assessment of “dual carbon” audit in power grid enterprises is implemented to show the two weighed projection techniques under q-ROFSs; and (4) comparative studies are constructed with existing techniques.

Comparative Analysis of Environmental Protection Provisions in Construction Procurement: A Case Study of Nepal's Projects Funded by National and International Agencies

This study investigates the environmental protection provisions embedded in procurement processes of construction projects in Nepal, funded by various national and international agencies. The research aims to compare and analyze the environmental safeguarding measures outlined in bidding documents from different funding sources, along with examining relevant legal frameworks and policies governing environmental protection in construction projects. Through a qualitative approach and content analysis methodology, the study delves into the scope, limitations, and significance of environmental considerations in construction procurement. Findings reveal diverse approaches across funding agencies, highlighting the emphasis on contractor responsibilities, safety measures, and project management. While Nepal's standard bidding documents establish foundational environmental provisions, projects funded by international agencies demonstrate a higher commitment to environmental sustainability. The study underscores the importance of comprehensive environmental measures in construction projects to mitigate ecological impact and promote long-term environmental conservation.

Projection hypothesis in the setting for the quantum Jarzynski equality

Projective quantum measurement is a theoretically accepted process in modern quantum mechanics. However, its projection hypothesis is widely regarded as an experimentally established empirical law. In this paper, we combine a previous result regarding the realization of a Hamiltonian process of the projection hypothesis in projective quantum measurement, where the complete set of the orbital observables of the center of mass of a macroscopic quantum mechanical system is restricted to a set of mutually commuting classical observables, and a previous result regarding the work required for an event reading (i.e. the informatical process in projective quantum measurement). Then, a quantum thermodynamic scheme is proposed for experimentally testing these two mutually independent theoretical results of projective quantum measurement simultaneously.

Compatibility of Generalized Noisy Qubit Measurements.

It is a crucial feature of quantum mechanics that not all measurements are compatible with each other. However, if measurements suffer from noise they may lose their incompatibility. Here, we consider the effect of white noise and determine the critical visibility such that all qubit measurements, i.e., all positive operator-valued measures (POVMs), become compatible, i.e., jointly measurable. In addition, we apply our methods to quantum steering and Bell nonlocality. We obtain a tight local hidden state model for two-qubit Werner states of visibility 1/2. This determines the exact steering bound for two-qubit Werner states and also provides a local hidden variable model that improves on previously known models. Interestingly, this proves that POVMs are not more powerful than projective measurements to demonstrate quantum steering for these states.

Extracting off-diagonal order from diagonal basis measurements

Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multiscale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments. Published by the American Physical Society 2024