Local asymptotic normality for finite dimensional quantum systems

DOI10.1007/s00220-009-0787-3zbMath1171.81005arXiv0804.3876OpenAlexW1976841091MaRDI QIDQ1028582

Jonas Kahn, Madalin I. Guta

Publication date: 6 July 2009

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.3876

Mathematics Subject Classification ID

Quantum computation (81P68) Quantum measurement theory, state operations, state preparations (81P15)

Related Items (30)

Minimax nonparametric estimation of pure quantum states ⋮ Quantum-state estimation problem via optimal design of experiments ⋮ A comparative study of estimation methods in quantum tomography ⋮ Uncertainty and trade-offs in quantum multiparameter estimation ⋮ Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics ⋮ Quantum local asymptotic normality based on a new quantum likelihood ratio ⋮ Attaining the ultimate precision limit in quantum state estimation ⋮ Geometry of quantum phase transitions ⋮ Asymptotic inference in system identification for the atom maser ⋮ Efficiency of estimators for locally asymptotically normal quantum statistical models ⋮ Quantum hypothesis testing for Gaussian states: quantum analogues of \(\chi ^{2}\), \(t\)-, and \(F\)-tests ⋮ Minimax estimation of low-rank quantum states and their linear functionals ⋮ A perspective on multiparameter quantum metrology: from theoretical tools to applications in quantum imaging ⋮ On quantumness in multi-parameter quantum estimation ⋮ Quantum learning: asymptotically optimal classification of qubit states ⋮ Rank-based model selection for multiple ions quantum tomography ⋮ Asymptotically optimal quantum channel reversal for qudit ensembles and multimode Gaussian states ⋮ Efficient tools for quantum metrology with uncorrelated noise ⋮ Spectral thresholding quantum tomography for low rank states ⋮ Protection of quantum Fisher information in entangled states via classical driving ⋮ Local asymptotic equivalence of pure states ensembles and quantum Gaussian white noise ⋮ Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics ⋮ Explicit formula for the Holevo bound for two-parameter qubit-state estimation problem ⋮ True precision limits in quantum metrology ⋮ Parameter estimation of qubit states with unknown phase parameter ⋮ Quantum U-statistics ⋮ Equivalence classes and local asymptotic normality in system identification for quantum Markov chains ⋮ Quantifying quantum correlations in noisy Gaussian channels ⋮ Fast state tomography with optimal error bounds ⋮ Multi-parameter estimation beyond quantum Fisher information

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic error rates in quantum hypothesis testing
• Mathematical theory of statistics. Statistical experiments and asymptotic decision theory
• Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
• Asymptotic methods in statistical decision theory
• Weak convergence and empirical processes. With applications to statistics
• Sufficiency in quantum statistical inference
• Optimal estimation of qubit states with continuous time measurements
• Local asymptotic normality in quantum statistics
• Optimum testing of multiple hypotheses in quantum detection theory
• Optimal multiple quantum statistical hypothesis testing
• Asymptotic Statistics
• Multiple-parameter quantum estimation and measurement of nonselfadjoint observables
• Optimal Extraction of Information from Finite Quantum Ensembles
• On Quantum Statistical Inference
• An Invitation to Quantum Tomography
• The rate of optimal purification procedures.

This page was built for publication: Local asymptotic normality for finite dimensional quantum systems