Fundamental Quantum Limit to Waveform Estimation

Mankei Tsang, Howard M. Wiseman, and Carlton M. Caves

Phys. Rev. Lett. 106, 090401 – Published 3 March 2011

Abstract

We derive a quantum Cramér-Rao bound (QCRB) on the error of estimating a time-changing signal. The QCRB provides a fundamental limit to the performance of general quantum sensors, such as gravitational-wave detectors, force sensors, and atomic magnetometers. We apply the QCRB to the problem of force estimation via continuous monitoring of the position of a harmonic oscillator, in which case the QCRB takes the form of a spectral uncertainty principle. The bound on the force-estimation error can be achieved by implementing quantum noise cancellation in the experimental setup and applying smoothing to the observations.

Received 18 October 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.090401

Authors & Affiliations

Mankei Tsang^1,*, Howard M. Wiseman², and Carlton M. Caves¹

¹Center for Quantum Information and Control, University of New Mexico, MSC07–4220, Albuquerque, New Mexico 87131-0001, USA
²Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia