Local asymptotic normality for qubit states

Local Asymptotic Normality Property for Lacunar Wavelet Series Multifractal Model

We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. T...

Local asymptotic normality for finite dimensional quantum systems

We extend our previous results on local asymptotic normality (LAN) for qubits [18, 15] to quantum systems of arbitrary finite dimension d. LAN means that the quantum statistical model consisting of n identically prepared d-dimensional systems with joint state ρ converges as n → ∞ to a statistical model consisting of classical and quantum Gaussian variables with fixed and known covariance matrix...

ar X iv : q ua nt - p h / 05 12 07 5 v 3 7 Ju n 20 06 Local asymptotic normality for qubit states

n of a fixed state ρ, 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 Tn (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 co...

Local Asymptotic Normality of Ranks and Covariates in Transformation Models

In this paper we exhibit an important but rather complicated example to which the Le Cam-Yang methods may, after some work, be applied. Semiparametric transformation models arise quite naturally in survival analysis. Specifically, let (Z1, T1), (Z2, T2), . . . , (Zn, Tn) be independent and identically distributed with Z, a vector of covariates, having distribution H, and T real. We suppose ther...

On the Preservation of Local Asymptotic Normality Under Information Loss