Minimax and adaptive estimation of the Wigner function in quantum homodyne tomography with noisy data

DOI10.1214/009053606000001488zbMath1117.62027arXivmath/0504058OpenAlexW2048902104MaRDI QIDQ995412

Luis Artiles, Cristina Butucea, Madalin I. Guta

Publication date: 3 September 2007

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504058

zbMATH Keywords

Radon transformWigner functiondeconvolutionadaptive estimationminimax risknonparametric estimationinfinitely differentiable functionsquantum stateexact constants in nonparametric smoothingquantum homodyne tomography

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Robustness and adaptive procedures (parametric inference) (62F35) Quantum optics (81V80) Applications of operator theory in probability theory and statistics (47N30)

Related Items

Minimax nonparametric estimation of pure quantum states, Optimal large-scale quantum state tomography with Pauli measurements, Bayesian estimation of the wave function, Adaptive sup-norm estimation of the Wigner function in noisy quantum homodyne tomography, Nonparametric goodness-of fit testing in quantum homodyne tomography with noisy data, Asymptotic equivalence of quantum state tomography and noisy matrix completion, Minimax estimation of the Wigner function in quantum homodyne tomography with ideal detectors, Nonparametric estimation of the purity of a quantum state in quantum homodyne tomography with noisy data, Relations between convergence rates in Schatten p-norms, Introduction to generation, manipulation and characterization of optical quantum states, Optimal estimation of qubit states with continuous time measurements, Local asymptotic normality in quantum statistics, Local asymptotic equivalence of pure states ensembles and quantum Gaussian white noise, Tests for qualitative features in the random coefficients model, Model selection for quantum homodyne tomography, Quantum computation and quantum information

Cites Work

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• Minimax theory of image reconstruction
• Speed of estimation in positron emission tomography and related inverse problems
• On the shape-from-moments problem and recovering edges from noisy Radon data
• Efficient estimation of a density in a problem of tomography.
• Minimax estimation of the Wigner function in quantum homodyne tomography with ideal detectors
• Sharp Optimality in Density Deconvolution with Dominating Bias. I
• Density Estimation for the Case of Supersmooth Measurement Error
• Noncommuting observables in quantum detection and estimation theory
• On the Quantum Correction For Thermodynamic Equilibrium
• Quantum and classical tomography with equidistant reference angles
• On Quantum Statistical Inference
• An Invitation to Quantum Tomography
• A Statistical Model for Positron Emission Tomography
• Coherent and Incoherent States of the Radiation Field