Preferred Measurements: Optimality and Stability in Quantum Parameter Estimation

Abstract

We explore precision in a measurement process incorporating pure probe states, unitary dynamics and complete measurements via a simple formalism. The concept of `information complement' is introduced. It undermines measurement precision and its minimization reveals the system properties at an optimal point. Maximally precise measurements can exhibit independence from the true value of the estimated parameter, but demanding this severely restricts the type of viable probe and dynamics, including the requirement that the Hamiltonian be block-diagonal in a basis of preferred measurements. The curvature of the information complement near a globally optimal point provides a new quantification of measurement stability.

4 pages, 2 figures, in submission. Substantial Extension and replacement of arXiv:0902.3260v1 in response to Referees' remarks

References in corpus (5)

• Generalized Limits for Single-Parameter Quantum Estimation
• Optimal phase measurements with pure Gaussian states
• All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry
• Local and Global Distinguishability in Quantum Interferometry
• Intrinsic metrological resolution as a distance measure and nonclassical light

Cited by in corpus (9)

• Control-enhanced multiparameter quantum estimation
• Quantum probes for the spectral properties of a classical environment
• Characterization of classical Gaussian processes using quantum probes
• Uncertainty limits for quantum metrology obtained from the statistics of weak measurements
• Quantum Phase Estimation with Entangled Photons produced by Parametric Down Conversion
• Generalizable control for multiparameter quantum metrology
• Optimal Conventional Measurements for Quantum-Enhanced Interferometry
• NOON-state formation from Fock-state Bose-Einstein condensates
• Phase Estimation with Non-Unitary Interferometers: Information as a Metric