arXiv subjects

Haidong Yuan

Publications and source records attributed to Haidong Yuan.

At least 19 recordsLinked to original sources

arXiv2026

Control incompatibility in multiparameter quantum metrology

In practical applications like quantum sensing and quantum imaging, there is often a necessity to estimate multiple parameters simultaneously. Although the ultimate precision limits for single-parameter estimation are well established, the precision limit of multi-parameter estimation is much less understood. This is primarily due to the inherent incompatibility of the optimal strategies for the estimation of different parameters, particularly those pertaining to optimal control.In this study, we tackle the critical issue of control incompatibility in multi-parameter estimation by presenting explicit cases that expose this challenge. Our research not only pioneers the exploration of control incompatibility but also highlights its pivotal role in the field. Furthermore, our work offers valuable insights into how to minimize trade-offs induced by control incompatibility and enhance precision. This paves the way for future investigations into control strategies that enable optimal estimation of multiple parameters that are incompatible.

quant-ph↗

arXiv2026

Optimal Hamiltonian Parameter Estimation in the Presence of Nuisance Parameters

In many sensing applications, the quantity of interest is not the only unknown, there are also additional unknown parameters, known as nuisance parameters, that affect the precision of estimation. While the ultimate local precision limit for a target parameter is well understood in the absence of nuisance parameters, the problem becomes significantly more challenging when they are present. In this work, we develop a framework for optimal Hamiltonian parameter estimation in the presence of nuisance parameters. We introduce an effective generator that captures the influence of nuisance parameters on the target precision, providing an explicit characterization of the ultimate precision limit for estimating the target parameter. Finally, we provide explicit optimal protocols, including probe state, control, and measurement that saturate this fundamental limit.

quant-ph↗

arXiv2026

Optimal Strategies for Multi-parameter Quantum Metrology

Estimating multiple unknown parameters simultaneously is essential for practical quantum sensing. However, it faces a fundamental challenge: the optimal strategy for estimating one parameter is often incompatible with that for another, making it impossible to simultaneously achieve the ultimate precision limits for all parameters. Here we develop a general and efficient computational framework that jointly optimizes probe states, control operations, and measurements across different strategy families, including parallel, sequential, and those with indefinite causal order. Our approach provides exact semidefinite-program formulations for several precision bounds, including the Holevo, Nagaoka-Hayashi, and quantum Cramér-Rao bounds. We demonstrate the capabilities of the framework in multiparameter magnetometry and frequency estimation, identifying optimal protocols within each class and revealing a strict hierarchy among the achievable performances of different classes in the multiparameter regime. The framework also directly incorporates resource constraints, such as energy budgets, enabling systematic investigation of experimentally realistic sensing scenarios. Furthermore, we develop a finite-memory optimization method for sequential strategies with restricted ancillary-memory dimension. By decomposing the protocol into initial probe preparation and intermediate control operations, this method provides a practical route to designing resource-constrained sequential sensing schemes. Our work establishes a versatile computational tool for determining fundamental precision limits and designing optimal quantum-sensing protocols in complex multiparameter settings.

quant-ph↗

arXiv2026

MathVis-Fine: Aligning Visual Supervision with Necessity via Progressive Dependency-Guided Training for Multimodal Mathematical Reasoning

Chain-of-Thought (CoT) reasoning has extended from purely linguistic domains to multimodal scenarios; however, existing approaches often treat visual inputs as homogeneous or auxiliary signals, failing to capture the intricate and sample-specific dependencies between text and images in mathematical problem-solving. This gives rise to two core issues: first, the supervisory signals for visual content are generalized and coarse-grained, lacking adaptation to the actual necessity of visual information in each sample; second, training feedback becomes inaccurate when visual rewards are uniformly applied without distinguishing the complementary relationships among inputs. These limitations hinder models from achieving precise multimodal reasoning. In this work, we propose a framework for modeling fine-grained visual dependencies in mathematical reasoning. We first construct the MathVis-Fine dataset, augmenting fine-grained visual annotations with visual dependency ratings. Building upon this dataset, we introduce a two-stage progressive visual enhancement training paradigm that balances answer correctness rewards and visual grounding rewards according to the intrinsic visual dependency level of each sample, thereby mitigating reward bias and improving supervision accuracy. Extensive experiments demonstrate that the MathVis-Fine framework effectively enhances visual perception progressively based on visual dependency, offering a more precise training framework for multimodal mathematical reasoning. We will release the dataset upon acceptance.

cs.AI↗

arXiv2026

Tight tradeoff relation and optimal measurement for multiparameter quantum estimation

In multiparameter quantum estimation, the optimal measurements for different parameters encoded in a quantum state are in general incompatible, giving rise to nontrivial tradeoffs between their attainable precisions. Understanding and characterizing such tradeoffs is essential for determining the ultimate precision limits in multiparameter quantum estimation and is therefore a central topic in quantum metrology. In this article, we present an approach that precisely quantifies the tradeoff resulting from incompatible optimal measurements in multiparameter estimation. We derive a tight analytical tradeoff relation that determines the ultimate precision limits for estimating an arbitrary number of parameters encoded in pure quantum states. Additionally, we provide a systematic methodology for constructing optimal measurements that saturate this tight bound in an analytical and structured manner. To demonstrate the power of our findings, we apply our methodology to quantum radar, resulting in a refined Arthurs-Kelly relation that characterizes the ultimate performance for the simultaneous estimation of range and velocity.

quant-ph↗

arXiv2026

Complementing Quantum Error Correction in Quantum Metrology via Swap Test

The precision and sensitivity achievable in quantum metrology are often compromised by the presence of noise. While quantum error correction has emerged as a promising strategy, it is ineffective in addressing noise that is indistinguishable from the signal. To address this challenge, virtual state purification was introduced as a complementary approach to quantum error correction. However, significant noise accumulation can impede its performance. To overcome this limitation, we propose a swap test-based method specifically designed to address indistinguishable noise, even under high noise levels. A systematic error-scaling analysis demonstrates that this method enables quantum-enhanced precision in certain scenarios. Furthermore, numerical simulations demonstrate that our method surpasses virtual state purification in both single- and multi-parameter estimation tasks. The significant improvements in precision across diverse settings underscore the robustness and practicality of our method for real-world applications.

quant-ph↗

arXiv2026

Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation

A fundamental challenge in multiparameter quantum estimation arises from the incompatibility of optimal measurements for different parameters, leading to intricate precision trade-offs that obscure the understanding of ultimate quantum limits. Here, we present an approach that precisely quantifies these trade-offs for an arbitrary number of parameters encoded in pure quantum states. Our approach not only derives tight analytical bounds for the trade-offs induced by measurement incompatibility but also provides a systematic methodology to design optimal measurement strategies that saturate these limits. To demonstrate the practical significance of our findings, we apply our framework to quantum radar and obtain a refined Arthurs-Kelly relation that characterizes the ultimate performance for the simultaneous estimation of range and velocity with any given amount of entanglement. This showcases the transformative potential of our findings for a wide range of applications in quantum metrology, sensing, and beyond.

quant-ph↗

arXiv2026

Controllable Spoken Dialogue Generation: An LLM-Driven Grading System for K-12 Non-Native English Learners

Large language models (LLMs) often fail to meet the pedagogical needs of K-12 English learners in non-native contexts due to a proficiency mismatch. To address this widespread challenge, we introduce a proficiency-aligned framework that adapts LLM outputs to learner abilities, using China's national curriculum (CSE) as a representative case. Our framework enables precise control over lexical complexity through a four-tier grading system, supported by a comprehensive suite of new resources: graded vocabulary lists and a multi-turn dialogue corpus. Our core technical contribution is the \textbf{DDPO} algorithm,Diversity Driven Policy Optimization, a multi-turn GRPO-based approach designed to preserve dialogue diversity while holistically optimizing dialogue quality. This method significantly outperforms conventional approaches, achieving low out-of-vocabulary rates and high diversity while enhancing conversational naturalness and pedagogical value. While grounded in the CSE, our framework is designed for flexibility and can be readily adapted to other educational standards. Our models, data, and code will all be open-sourced, providing a scalable platform for personalized English speaking practice that effectively addresses the unique challenges faced by K-12 learners in non-immersive environments.

cs.CL↗

arXiv2026

Thinking with Constructions: A Benchmark and Policy Optimization for Visual-Text Interleaved Geometric Reasoning

Geometric reasoning inherently requires "thinking with constructions" -- the dynamic manipulation of visual aids to bridge the gap between problem conditions and solutions. However, existing Multimodal Large Language Models (MLLMs) are largely confined to passive inference with static diagrams, lacking the strategic knowledge of when and how to construct effective visual aids. To address this, we present a framework for Visual-Text Interleaved Chain-of-Thought. We first introduce GeoAux-Bench, the first benchmark comprising 4,334 geometry problems that aligns textual construction steps with ground-truth visual updates. Our pilot study reveals two critical insights: (1) interleaved visual-textual aids outperform single-modality counterparts, which cannot losslessly capture geometric synergy; and (2) valid constructions act as entropy reducers, strongly correlating with reduced reasoning perplexity. Building on these findings, we propose Action Applicability Policy Optimization (A2PO), a reinforcement learning paradigm for mastering strategic construction. A2PO employs Adaptive Reward Shaping to regulate the timing and quality of visual aids via counterfactual sampling to distinguish necessary from redundant constructions. Experiments demonstrate our approach enables MLLMs to leverage selective auxiliary constructions, yielding a 3.51% gain over strong baselines. Code and data are available on GitHub.

cs.AI↗

arXiv2026

Distributed multi-parameter quantum metrology with a superconducting quantum network

Quantum metrology has emerged as a powerful tool for timekeeping, field sensing, and precision measurements in fundamental physics. With the advent of distributed quantum metrology, its capabilities have extended to probing spatially distributed parameters across networked quantum systems. However, scalable implementations of distributed quantum metrology with multi-parameter estimation remain limited, particularly due to the challenges of generating and distributing entanglement across a quantum network and dealing with incompatibilities in multi-parameter quantum metrology. Here we demonstrate distributed multi-parameter quantum metrology on a modular superconducting quantum network with low-loss microwave interconnects, a platform that uniquely combines fast gate operations, adaptive control, and deterministic non-local entanglement generation. Using a control-enhanced sequential protocol, we estimate all three components of a remote vector field, achieving up to 13.72 dB improvement in precision over the individual strategy. We further perform direct estimation of vector field gradients along two directions across spatially separated nodes, realizing a 3.44 dB gain over local entanglement strategies. These results establish superconducting quantum networks as a competitive and reconfigurable platform for scalable multi-parameter distributed quantum metrology.

quant-ph↗

arXiv2026

Approaching the Limit in Multiparameter AC Magnetometry with Quantum Control

Simultaneously estimating multiple parameters at the ultimate limit is a central challenge in quantum metrology, often hindered by inherent incompatibilities in optimal estimation strategies. At its most extreme, this incompatibility culminates in a fundamental impossibility when the quantum Fisher information matrix (QFIM) becomes singular, rendering joint estimation unattainable. This is the case for a canonical problem: estimating the amplitude and frequency of an AC magnetic field, where the generators are parallel to each other. Here, we introduce a quantum control protocol that resolves this singularity. Our control protocol strategically engineers the sensor's time evolution so the generators for the two parameters become orthogonal. It not only removes the singularity but also restores the optimal scaling of precision with interrogation time for both parameters simultaneously. We experimentally validate this protocol using a nitrogen-vacancy center in diamond at room temperature, demonstrating the concurrent achievement of the optimal scaling for both parameters under realistic conditions.

quant-ph↗

arXiv2025

Optimal Control of Coupled Sensor-Ancilla Qubits for Multiparameter Estimation

Designing optimal control for multiparameter quantum sensing is essential for approaching the ultimate precision limits. However, analytical solutions are generally available only for simple systems, while realistic scenarios often involve coupled qubits and time-dependent Hamiltonians. Here we numerically investigate optimal control of a two-qubit sensor-ancilla system coupled via an Ising term using Gradient Ascent Pulse Engineering (GRAPE) to minimize the objective function. By seeding the optimization recursively with solutions obtained for smaller coupling strengths and selecting a suitable initial guess, we achieve robust convergence and high precision across a wide range of interaction strengths and field configurations. The proposed approach offers a practical route toward high-sensitivity, robust multiparameter magnetometry and it is applicable to solid-state quantum sensors such as nitrogen-vacancy (NV) centers in realistic experimental settings.

quant-ph↗

arXiv2025

Error-mitigated quantum metrology via enhanced virtual purification

Quantum metrology stands as a leading application of quantum science and technology, yet noise often constrains its precision and sensitivity. In near-term quantum metrology, existing protocols largely depend on virtual state purification, but significant noise accumulation and additional noise from the implementations of these protocols can impede their effectiveness. We propose enhanced virtual channel purification to address these problems, yielding enhanced virtual state purification as a by-product. Within sequential quantum metrology schemes, our error analysis reveals substantial bias reduction and quantum advantages in sampling cost when the number of encoding channels is ${\mathcal{O}}(p^{-1})$, where $p$ represents the error rate of encoding channels. In this range, our methods demonstrate significant improvements in parameter estimation precision and robustness against practical noise, as evidenced by numerical simulations for both single- and multi-parameter tasks. Particularly, these methods can naturally extend beyond quantum metrology, indicating their broad applicability in quantum information and quantum computation.

quant-ph↗

arXiv2025

Nonreciprocity enhanced Quantum Gyroscopes based on Surface Acoustic Waves

Surface acoustic waves (SAWs), as Rayleigh waves generated by elastic media, have been used in gyroscopes for over 40 years due to their unique propagation characteristics. However, their working principle, based on Coriolis effects, has become increasingly ineffective for addressing modern sensing challenges in complex scenarios. Fortunately, recent advancements in quantized SAWs offer a promising solution: SAWs operating at extremely low pump powers (approximately at the single-phonon level) can exhibit substantial quantum coherence, enabling investigations into the fundamental limits of SAW gyroscopes as constrained by the Heisenberg uncertainty relation. In particular, when multiple SAWs couple to a common waveguide at distinct locations, the nonlocality arising from the spatial separation among coupling points induces directional coupling between the SAWs. To elucidate this directionality, we propose a quantum gyroscope characterized by multiplepoint couplings. Unlike traditional single-point coupling designs, our gyroscope exhibits distinctive time-delayed dynamics that depend on the system's topologies. We emphasize that these dynamics invalidate the Markovian approximation, even when the time delay is relatively small. Through a comprehensive analysis of all possible topologies, we observe that the directional coupling implies an inherent nonreciprocal transfer. This nonreciprocity confers signiffcant advantages to our gyroscope compared to traditional designs, notably enhancing both the signal-to-noise ratio and sensitivity. Speciffcally, it enables the extraction of output signals that would otherwise be obscured by noise. Consequently, our ffndings suggest that systems with multiple-point couplings and the associated nonreciprocity can serve as valuable resources for advancing quantum sensing technologies.

quant-ph↗

arXiv2025

Quantum hypothesis testing via robust quantum control

Quantum hypothesis testing plays a pivotal role in quantum technologies, making decisions or drawing conclusions about quantum systems based on observed data. Recently, quantum control techniques have been successfully applied to quantum hypothesis testing, enabling the reduction of error probabilities in the task of distinguishing magnetic fields in presence of environmental noise. In real-world physical systems, such control is prone to various channels of inaccuracies. Therefore improving the robustness of quantum control in the context of quantum hypothesis testing is crucial. In this work, we utilize optimal control methods to compare scenarios with and without accounting for the effects of signal frequency inaccuracies. For parallel dephasing and spontaneous emission, the optimal control inherently demonstrates a certain level of robustness, while in the case of transverse dephasing with an imperfect signal, it may result in a higher error probability compared to the uncontrolled scheme. To overcome these limitations, we introduce a robust control approach optimized for a range of signal noise, demonstrating superior robustness beyond the predefined tolerance window. On average, both the optimal control and robust control show improvements over the uncontrolled schemes for various dephasing or decay rates, with the robust control yielding the lowest error probability.

quant-ph↗

arXiv2025

Optimal scheme for distributed quantum metrology

Optimal strategies for local quantum metrology -- including the preparation of optimal probe states, implementation of optimal control and measurement strategies, are well established. However, for distributed quantum metrology, where the goal is to estimate global properties of multiple spatially distributed parameters, the optimal scheme -- particularly the role of optimal control -- remains poorly understood. In this work, we address this challenge by developing optimal schemes for distributed quantum metrology that characterize the ultimate precision limits in distributed systems. We derive the optimal probe state, optimal control protocols, and measurement strategies in estimating a linear combination of $N$ independent unknown parameters coupled to $d$ networked sensors. Crucially, we prove that the optimal control operations can be implemented locally on each sensor, eliminating the need for non-local control operations across distant nodes. This result significantly reduces the complexity of implementing optimal strategies in distributed quantum metrology. To demonstrate the power of our framework, we apply it to several key scenarios.

quant-ph↗

arXiv2025

Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime

Non-Hermitian quantum metrology, an emerging field at the intersection of quantum estimation and non-Hermitian physics, holds promise for revolutionizing precision measurement. Here, we present a comprehensive investigation of non-Hermitian quantum parameter estimation in the quantum regime, with a special focus on achieving Heisenberg scaling. We introduce a concise expression for the quantum Fisher information (QFI) that applies to general non-Hermitian Hamiltonians, enabling the analysis of estimation precision in these systems. Our findings unveil the remarkable potential of non-Hermitian systems to attain the Heisenberg scaling of $1/t$, where $t$ represents time. Moreover, we derive optimal measurement conditions based on the proposed QFI expression, demonstrating the attainment of the quantum Cramér-Rao bound. By constructing non-unitary evolutions governed by two non-Hermitian Hamiltonians, one with parity-time symmetry and the other without specific symmetries, we experimentally validate our theoretical analysis. The experimental results affirm the realization of Heisenberg scaling in estimation precision, marking a substantial milestone in non-Hermitian quantum metrology.

quant-ph↗

arXiv2025

Tight bounds of quantum speed limit for noisy dynamics via maximum rotation angles

The laws of quantum physics place a limit on the speed of computation. In particular, the evolution time of a system from an initial state to a final state cannot be arbitrarily short. Bounds on the speed of evolution for unitary dynamics have long been studied. A few bounds on the speed of evolution for noisy dynamics have also been obtained recently, which are, however, not tight. In this paper, we present a new framework for quantum speed limit concerning noisy dynamics. Within this framework, we obtain the exact maximum rotation angle that noisy dynamics can achieve at any given time, which gives rise to a tight bound on the evolution time for noisy dynamics. The bound obtained through semi-definite programming highlights the fundamental differences between noisy dynamics and unitary dynamics. Furthermore, we show that the \textit{orthogonalization} time, defined as the minimum time required to evolve any initial state to a state with zero fidelity with respect to the initial state, is generally not applicable to noisy dynamics.

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