Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics

Information Geometry Approach to Parameter Estimation in Hidden Markov Models

We consider the estimation of hidden Markovian process by using information geometry with respect to transition matrices. We consider the case when we use only the histogram of k-memory data. Firstly, we focus on a partial observation model with Markovian process and we show that the asymptotic estimation error of this model is given as the inverse of projective Fisher information of transition...

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...

On the Preservation of Local Asymptotic Normality Under Information Loss

Asymptotic Estimation of Shift Parameter of a Quantum State∗

The rise of quantum estimation theory dates back to the late 1960s – 1970s (see [8], [9]). It was initially developed as an adequate mathematical framework for design of optimal receiver in quantum communication channels, and later turned out to be relevant also for clarification of some foundational issues of quantum measurement. New interest to quantum estimation theory was brought by the dev...

Asymptotic Normality in Density Support Estimation

Estimation Gérard BIAU a,∗, Benôıt CADRE b, David M. MASON c and Bruno PELLETIER d a LSTA & LPMA Université Pierre et Marie Curie – Paris VI Bôıte 158, 175 rue du Chevaleret 75013 Paris, France [email protected] b IRMAR, ENS Cachan Bretagne, CNRS, UEB Campus de Ker Lann Avenue Robert Schuman 35170 Bruz, France [email protected] c University of Delaware Food and Resource Econ...