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Fundamental Quantum Limit to Waveform Estimation · Around

2010

Fundamental Quantum Limit to Waveform Estimation

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

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We derive a quantum Cram\'er-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.

Built on

V. B. Braginsky and F. Ya. Khalili, Quantum Measurement
1980
Earlier work this paper cites.
C. W. Helstrom, Quantum Detection and Estimation Theory
1982
Earlier work this paper cites.
K. Kraus, States, Effects, and Operations: Fundamental Notions of Quantum Theory
1983
Earlier work this paper cites.
H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part I
2001
Earlier work this paper cites.

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Then

M. Tsang, Phys. Rev. Lett. 102
2010
Closest in time.
M. Tsang and C. M. Caves, Phys. Rev. Lett. 105
2010
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W. G. Unruh, in Quantum Optics, Experimental Gravitation, and Measurement Theory
2010
Closest in time.

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