Quantum metrology beyond the Quantum Cram\'er-Rao theorem

TL;DR

This paper explores quantum estimation scenarios where traditional assumptions do not hold, revealing that quantum-enhanced measurements can surpass previous precision bounds by developing an alternative approach beyond the Quantum Cramér-Rao theorem.

Contribution

It introduces a new framework for quantum estimation when measurement strategies depend on the unknown parameter, challenging the standard quantum Cramér-Rao bounds.

Findings

Quantum measurement strategies can be intrinsically parameter-dependent.

Quantum-enhanced measurements may achieve higher precision than traditional bounds.

The study provides a new perspective on quantum metrology beyond standard assumptions.

Abstract

A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter itself. This assumption is crucial to prove the quantum Cram\'er-Rao theorem and to introduce the quantum Fisher information as an upper bound to the Fisher information of any possible measurement. However, there are relevant estimation problems where this assumption does not hold and an alternative approach should be developed to find the genuine ultimate bound to precision of quantum measurements. We investigate physical situations where there is an intrinsic dependence of the measurement strategy on the parameter and find that quantum-enhanced measurements may be more precise than previously thought.