Local asymptotic normality for qubit states
arXiv:quant-ph/0512075 · doi:10.1103/PhysRevA.73.052108
Abstract
We consider n identically prepared qubits and study the asymptotic properties of the joint state ρ^{\otimes n}. We show that for all individual states ρsituated in a local neighborhood of size 1/\sqrt{n} of a fixed state ρ^0, the joint state converges to a displaced thermal equilibrium state of a quantum harmonic oscillator. The precise meaning of the convergence is that there exist physical transformations T_{n} (trace preserving quantum channels) which map the qubits states asymptotically close to their corresponding oscillator state, uniformly over all states in the local neighborhood. A few consequences of the main result are derived. We show that the optimal joint measurement in the Bayesian set-up is also optimal within the pointwise approach. Moreover, this measurement converges to the heterodyne measurement which is the optimal joint measurement of position and momentum for the quantum oscillator. A problem of local state discrimination is solved using local asymptotic normality.
16 pages, 3 figures, published version
References in corpus (1)
Cited by in corpus (62)
- A Geometric Perspective on Quantum Parameter Estimation
- Sample-optimal tomography of quantum states
- Large gradients via correlation in random parameterized quantum circuits
- Choice of Measurement Sets in Qubit Tomography
- Local asymptotic normality for finite dimensional quantum systems
- Evaluating the Holevo Cramér-Rao bound for multi-parameter quantum metrology
- Tutorial: Optical quantum metrology
- Quantum local asymptotic normality based on a new quantum likelihood ratio
- Attaining the ultimate precision limit in quantum state estimation
- Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation
- On Asymptotic Quantum Statistical Inference
- Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation
- Explicit formula for the Holevo bound for two-parameter qubit estimation problem
- Tight bounds on the simultaneous estimation of incompatible parameters
- Local asymptotic normality in quantum statistics
- Fisher information and asymptotic normality in system identification for quantum Markov chains
- Ultimate precision of joint quadrature parameter estimation with a Gaussian probe
- Classification and characterization of quantum parametric models in quantum estimation theory
- Incompatibility in Quantum Parameter Estimation
- Quantum learning: optimal classification of qubit states
- Imaginarity-free quantum multiparameter estimation
- Optimal estimation of qubit states with continuous time measurements
- On the quantumness of multiparameter estimation problems for qubit systems
- Quantum learning of coherent states
- On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation
- Equivalence classes and local asymptotic normality in system identification for quantum Markov chains
- Parameter estimation and system identification for continuously-observed quantum systems
- Fourier Analytic Approach to Phase Estimation
- Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics
- Precision bounds in noisy quantum metrology
- Asymptotic inference in system identification for the atom maser
- Conciliation of Bayes and Pointwise Quantum State Estimation: Asymptotic information bounds in quantum statistics
- Minimax quantum tomography: the ultimate bounds on accuracy
- Quantum teleportation benchmarks for independent and identically-distributed spin states and displaced thermal states
- Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective
- Fourier Analytic Approach to Quantum Estimation of Group Action
- Compression for quantum population coding
- Optimal cloning of mixed Gaussian states
- Multiparameter estimation for qubit states with collective measurements: a case study
- RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels
- Maximum logarithmic derivative bound on quantum state estimation as a dual of the Holevo bound
- Asymptotically optimal purification and dilution of mixed qubit and Gaussian states
- Maximum likelihood versus likelihood-free quantum system identification in the atom maser
- Local asymptotic equivalence of pure quantum states ensembles and quantum Gaussian white noise
- Quantum hypothesis testing for quantum Gaussian states: Quantum analogues of chi-square, t and F tests
- Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
- Efficiency of estimators for locally asymptotically normal quantum statistical models
- Achieving the Multi-parameter Quantum Cramér-Rao Bound with Antiunitary Symmetry
- Quantum U-statistics
- Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise
- Stochastic behavior of outcome of Schur-Weyl duality measurement
- Asymptotically optimal quantum channel reversal for qudit ensembles and multimode Gaussian states
- Minimax estimation of qubit states with Bures risk
- Topics in Estimation of Quantum Channels
- An approximate quantum Cramér--Rao bound based on skew information
- Efficient trainability of linear optical modules in quantum optical neural networks
- Estimating quantum Markov chains using coherent absorber post-processing and pattern counting estimator
- Measurement compatibility in multiparameter quantum interferometry
- Approaching the Multiparameter Quantum Cramér-Rao Bound via Classical Correlation and Entangling Measurements
- Compression of quantum shallow-circuit states
- Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics
- Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group