Quantum estimation of unknown parameters

Seminar date and time: 
Wednesday, 25 October, 2017 - 14:30
Esteban Martínez Vargas
GIQ Seminar Room

There seems to be a persistent problem in the field of Quantum Metrology: Quantum Fisher Information is well defined only for an infinite amount of resources, via an adaptive measurement scheme. We state a theoretical framework that avoids this issue, which is based on a Bayesian parameter estimation scheme. Although the Bayesian approach have already been made in the field, we introduced a modified bound which entails taking the maximization over all POVMs for the Van Trees Information instead of the Fisher Information (i.e. outside the Integral) because the parameter is a random variable. This modified bound beats the maximum likelihood method in a Bayesian Inference scheme for a specific example. Another important issue for Quantum Metrology is that the relevant bounds are normally hard to calculate. This is because this bounds normally requires a maximization over a complicated set (the POVM set). We addressed this problem also, with a general numerical method that is efficient. We present some analytical calculations for our modified bound.

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