On Asymptotic Quantum Statistical Inference

Abstract

We study asymptotically optimal statistical inference concerning the unknown state of $N$ identical quantum systems, using two complementary approaches: a "poor man's approach" based on the van Trees inequality, and a rather more sophisticated approach using the recently developed quantum form of LeCam's theory of Local Asymptotic Normality.

34 pages. to appear in `From Probability to Statistics and Back: High-Dimensional Models and Processes'. A Festschrift in Honor of Jon Wellner. Edited by Banerjee, M., Bunea, F., Huang, J., Maathuis, M. and Koltchinskii, V. extension of a previous paper arXiv:math/0512443

References in corpus (4)

• On Asymptotic Quantum Statistical Inference
• Fisher information and asymptotic normality in system identification for quantum Markov chains
• Asymptotic performance of optimal state estimation in quantum two level system
• Quantum teleportation benchmarks for independent and identically-distributed spin states and displaced thermal states

Cited by in corpus (29)

• Compatibility in Multiparameter Quantum Metrology
• Multi-parameter Quantum Metrology
• Multi-parameter estimation beyond Quantum Fisher Information
• On quantumness in multi-parameter quantum estimation
• True precision limits in quantum metrology
• Quantum local asymptotic normality based on a new quantum likelihood ratio
• Quantum interferometry with three-dimensional geometry
• Attaining the ultimate precision limit in quantum state estimation
• Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation
• On Asymptotic Quantum Statistical Inference
• Tight bounds on the simultaneous estimation of incompatible parameters
• Optimal measurements for quantum spatial superresolution
• Symmetric Logarithmic Derivative of Fermionic Gaussian States
• A family of generalized quantum entropies: definition and properties
• Rank-based model selection for multiple ions quantum tomography
• The Holevo Cramér-Rao bound is at most thrice the Helstrom version
• Quantum Zeno effect in parameter estimation
• Conservative classical and quantum resolution limits for incoherent imaging
• Quantum learning of coherent states
• A comparative study of estimation methods in quantum tomography
• Optimal Quantum Metrology of Distant Black Bodies
• Quantum Weiss-Weinstein bounds for quantum metrology
• Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics
• Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective
• Physics-inspired forms of the Bayesian Cramér-Rao bound
• Local asymptotic equivalence of pure quantum states ensembles and quantum Gaussian white noise
• Efficiency of estimators for locally asymptotically normal quantum statistical models
• Non-asymptotic quantum metrology
• Estimating quantum Markov chains using coherent absorber post-processing and pattern counting estimator