Bounds on quantum multiple-parameter estimation with Gaussian state

Quantum parameter estimation using general single-mode Gaussian states

Ziv-Zakai error bounds for quantum parameter estimation.

I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cramér-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a Heisenberg error limit that scales with the average energy and a limit similar to the quantum Cramér-Rao bound that scales with the energy variance. These results are further illustrated by ap...

Parameter Estimation in Spatial Generalized Linear Mixed Models with Skew Gaussian Random Effects using Laplace Approximation

 Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...

Quantum Limits on Parameter Estimation

We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1–3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most experimentally accessible situations, where multiple rounds of measurements, auxiliary systems or external control of the evolution are available. The proof pr...

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...