A general estimation framework for continuous-variable systems

• URL: http://arxiv.org/abs/2607.19287v1
• Date: Tue, 21 Jul 2026 16:58:41 GMT
• Title: A general estimation framework for continuous-variable systems
• Abstract summary: We show that informational completeness does not guarantee statistically stable reconstruction from finite measurement data.<n>We develop a general estimation theory for continuous-variable systems in which stable reconstructibility is characterized by the POVM effects forming a measurement frame.
• Score: 32.505127447635864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that informational completeness, while sufficient to have a bijection between ideal measurement probabilities and quantum states, does not guarantee statistically stable reconstruction from finite measurement data. To address this problem, we develop a general estimation theory for continuous-variable systems in which stable reconstructibility is characterized by the POVM effects forming a measurement frame. Informational completeness is therefore necessary, but not sufficient, for stable reconstruction. Our framework is based on measurement frames in a $σ$-regularized operator geometry, where the reference state $σ$ encodes prior information about relevant features of the measured states. For any fixed measurement scheme, observables may be inaccessible, weakly reconstructible only through estimators with divergent variance, or stably reconstructible by finite-variance unbiased estimators. The relevant regime is determined by the range of the POVM synthesis operator. Our framework provides practical methods for constructing estimators and gives an operational interpretation of singular quasiprobability distributions, including the Glauber-Sudarshan $P$ representation: quasiprobabilities act as unbiased estimators for associated observables, and their singularities reflect a pathological feature of the corresponding measurement: its lack of loewr frame bound. We furthermore show how this formalism naturally provides operational regularization procedures tied to prior information. Overall, our framework provides a unified view of continuous-variable tomography, quasiprobability representations, and classical-shadow estimation.

Related papers

• Orthogonal JEPA: Factorized Predictive States for Latent World Models [95.20158869896393]
  We introduce method, a latent world-modeling framework based on predictive factorization.<n>We show that method can allocate redundant capacity to dominant signals while providing weak or conflicting gradients to less dominant predictive structure.<n>Experiments on controlled vision, single-cell transcriptomics, longitudinal health records, continuous control, and molecular dynamics evaluate representation quality, forecasting, planning, and long-horizon stability.
  arXiv  Detail & Related papers  (2026-08-20T13:59:57Z)
• ARC: Adaptive Robust Joint State and Covariance Estimation [42.045109659898465]
  Sensor measurements are frequently corrupted by outliers and non-Gaussian noise.<n>These imperfections in the sensor data can cause classical state estimators to generate biased and unreliable state and uncertainty estimates.<n>This paper proposes a unified Block-Coordinate Descent framework that combines a norm-aware adaptive robust loss, and an Iteratively Reweighted Least-Squares state update.
  arXiv  Detail & Related papers  (2026-06-18T16:09:50Z)
• Non-Parametric Rehearsal Learning via Conditional Mean Embeddings [88.89267783967263]
  We propose a non-parametric rehearsal learning approach for textitavoiding undesired future (AUF) problems.<n>Specifically, we use kernel machinery to reformulate the AUF objective into a unified representation that disentangles desirability modeling from action-induced distributional changes.
  arXiv  Detail & Related papers  (2026-05-09T15:30:52Z)
• Noise Titration: Exact Distributional Benchmarking for Probabilistic Time Series Forecasting [1.5939955861266883]
  We propose a paradigm shift toward interventionist, exact-statistical benchmarking.<n>We transform forecasting from a black-box sequence matching game into an exact distributional inference task.<n>We find that state-of-the-art zero-shot models behave consistently with the context-parroting mechanism.
  arXiv  Detail & Related papers  (2026-03-23T17:14:11Z)
• Robust Sequential Tracking via Bounded Information Geometry and Non-Parametric Field Actions [0.0]
  Empirical benchmarks across three domains--LiDAR maneuvering target tracking, high-frequency cryptocurrency order flow, and quantum state tomography--demonstrate that this information geometry analytically truncates outliers.
  arXiv  Detail & Related papers  (2026-03-13T21:40:44Z)
• A Realistic Framework for Quantum Sensing under Finite Resources [0.0]
  Quantum-enhanced sensing is commonly benchmarked using the quantum Fisher information (QFI)<n>Here we establish a realistic end-to-end framework for quantum sensing under finite resources.
  arXiv  Detail & Related papers  (2026-03-09T12:28:51Z)
• Revisiting Multivariate Time Series Forecasting with Missing Values [65.30332997607141]
  Missing values are common in real-world time series.<n>Current approaches have developed an imputation-then-prediction framework that uses imputation modules to fill in missing values, followed by forecasting on the imputed data.<n>This framework overlooks a critical issue: there is no ground truth for the missing values, making the imputation process susceptible to errors that can degrade prediction accuracy.<n>We introduce Consistency-Regularized Information Bottleneck (CRIB), a novel framework built on the Information Bottleneck principle.
  arXiv  Detail & Related papers  (2025-09-27T20:57:48Z)
• Equivariant Representation Learning for Symmetry-Aware Inference with Guarantees [20.285132886770146]
  We introduce an equivariant representation learning framework that simultaneously addresses regression, conditional probability estimation, and uncertainty quantification.<n>Grounded in operator and group representation theory, our framework approximates the spectral decomposition of the conditional expectation operator.<n> Empirical evaluations on synthetic datasets and real-world robotics applications confirm the potential of our approach.
  arXiv  Detail & Related papers  (2025-05-26T10:47:23Z)
• Measuring and Modeling Uncertainty Degree for Monocular Depth Estimation [50.920911532133154]
  The intrinsic ill-posedness and ordinal-sensitive nature of monocular depth estimation (MDE) models pose major challenges to the estimation of uncertainty degree. We propose to model the uncertainty of MDE models from the perspective of the inherent probability distributions. By simply introducing additional training regularization terms, our model, with surprisingly simple formations and without requiring extra modules or multiple inferences, can provide uncertainty estimations with state-of-the-art reliability.
  arXiv  Detail & Related papers  (2023-07-19T12:11:15Z)
• A Robustness Analysis of Blind Source Separation [91.3755431537592]
  Blind source separation (BSS) aims to recover an unobserved signal from its mixture $X=f(S)$ under the condition that the transformation $f$ is invertible but unknown. We present a general framework for analysing such violations and quantifying their impact on the blind recovery of $S$ from $X$. We show that a generic BSS-solution in response to general deviations from its defining structural assumptions can be profitably analysed in the form of explicit continuity guarantees.
  arXiv  Detail & Related papers  (2023-03-17T16:30:51Z)
• Non-Linear Spectral Dimensionality Reduction Under Uncertainty [107.01839211235583]
  We propose a new dimensionality reduction framework, called NGEU, which leverages uncertainty information and directly extends several traditional approaches. We show that the proposed NGEU formulation exhibits a global closed-form solution, and we analyze, based on the Rademacher complexity, how the underlying uncertainties theoretically affect the generalization ability of the framework.
  arXiv  Detail & Related papers  (2022-02-09T19:01:33Z)
• GenDICE: Generalized Offline Estimation of Stationary Values [108.17309783125398]
  We show that effective estimation can still be achieved in important applications. Our approach is based on estimating a ratio that corrects for the discrepancy between the stationary and empirical distributions. The resulting algorithm, GenDICE, is straightforward and effective.
  arXiv  Detail & Related papers  (2020-02-21T00:27:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.