title: Fundamental quantum limit to waveform estimation.
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.
authors.affiliation: Center for Quantum Information and Control, University of New Mexico, Albuquerque, 87131-0001, USA.
authors.forename: Mankei
authors.initials: M
authors.lastname: Tsang
authors.forename: Howard M
authors.initials: HM
authors.lastname: Wiseman
authors.forename: Carlton M
authors.initials: CM
authors.lastname: Caves