Quantum measurement bounds beyond the uncertainty relations

TL;DR

This paper introduces a new bound on parameter estimation precision that extends traditional uncertainty relations by relating it to the expectation value of an observable, surpassing variance-based limits.

Contribution

It presents a novel bound on measurement precision based on the expectation value, extending the Cramer-Rao inequality and Heisenberg uncertainty principles.

Findings

New bound on estimation precision in quantum measurements

Extension of Cramer-Rao inequality and Heisenberg uncertainty relation

Provides tighter limits for quantum parameter estimation

Abstract

We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision is typically bounded in terms of the variance of an observable.