Attainability of the quantum information bound in pure state models

Abstract

The attainability of the quantum Cramér-Rao bound [QCR], the ultimate limit in the precision of the estimation of a physical parameter, requires the saturation of the quantum information bound [QIB]. This occurs when the Fisher information associated to a given measurement on the quantum state of a system which encodes the information about the parameter coincides with the quantum Fisher information associated to that quantum state. Braunstein and Caves [PRL {\bf 72}, 3439 (1994)] have shown that the QIB can always be achieved via a projective measurement in the eigenvectors basis of an observable called symmetric logarithmic derivative. However, such projective measurement depends, in general, on the value of the parameter to be estimated. Requiring, therefore, the previous knowledge of the quantity one is trying to estimate. For this reason, it is important to investigate under which situation it is possible to saturate the QCR without previous information about the parameter to be estimated. Here, we show the complete solution to the problem of which are all the initial pure states and the projective measurements that allow the global saturation of the QIB, without the knowledge of the true value of the parameter, when the information about the parameter is encoded in the system by a unitary process.

References in corpus (2)

• Optimal adaptive control for quantum metrology with time-dependent Hamiltonians
• All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry

Cited by in corpus (7)

• Qubit-channel metrology with very noisy initial states
• Efficient qubit phase estimation using adaptive measurements
• Role of indistinguishability in interferometric phase estimation
• Bayesian and frequentist estimators for the transition frequency of a driven two-level quantum system
• Usefulness of Quantum Entanglement for Enhancing Precision in Frequency Estimation
• Information geometric approach to mixed state quantum estimation
• Noisy initial-state qubit-channel metrology with additional undesirable noisy evolution