Quantum local asymptotic normality based on a new quantum likelihood ratio

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...

Asymptotic normality of the maximum likelihood

We present conditions to obtain the asymptotic normality of the maximum likelihood estimator of a loss process presented in [2]. We shall use the notations of [2], write ‖ · ‖q for the standard L norm on an arbitrary space R, d ≥ 1, and let D φ denote the k−th order di erentiation with respect to φ. Let us introduce the following hypotheses: (A4) For all i ∈ {1, . . . , r}, λi(Φ0) > 0. (A5) For...

An Empirical Likelihood Ratio Test for Normality

The empirical likelihood ratio (ELR) test for the problem of testing for normality is derived in this paper. The sampling properties of the ELR test and four other commonly used tests are provided and analyzed using the Monte Carlo simulation technique. The power comparisons against a wide range of alternative distributions show that the ELR test is the most powerful of these tests in certain s...

Designing and analyzing the quantum efficiency model based on quantum immaterial skills through thematic analysis

The aim of this study was to identify the components of productivity based on intangible quantum skills and provide a model of quantum productivity. This research is fundamental and applied in terms of purpose, which has been done by analytical, exploratory and field methods. The statistical population of the present study was professors and experts in the field of sports management and manager...

On the Preservation of Local Asymptotic Normality Under Information Loss