Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals

Abstract

The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational-wave detectors.

Quantum expander for gravitational-wave observatories

“…variational readout). We prove that the condition (ii) is satisfied by directly computing the QCRB in the case of GW detectors is defined as follows [15]:…”

“…when ω s ∼ ω F SR . It also takes into account the effects of quantum radiation pressure noise, quantum decoherence, the next free spectral ranges of the cavities as well as the response function of the detector to gravitational waves.The sensitivity of any gravitational-wave observatory is ultimately limited by its quantum Cramer-Rao bound (QCRB) S QCRB h (Ω)[15]. The conditions for reaching its quantum Cramer-Rao bound are that (i) the quantum radiation pressure noise is evaded, and (ii) theSignal frequency, (Hz) Quantum noise normalized to strain signals of 10 -24 (1/√Hz) FIG.…”

Converting the signal-recycling cavity into an unstable optomechanical filter to enhance the detection bandwidth of gravitational-wave detectors

“…We can follow the same process as above to find the thermal noise fluctuations arising from thermal noise quadrature operatorsb th 1,2 , noting that the spectral density for the heat bath is given by Eq. (14).…”

“…The arm cavities also resonantly enhance the carrier and increase the intracavity intensity, thereby reducing the relative photon number uncertainty and thus the shot noise. However, there exists a strict trade-off between the peak sensitivity and detection bandwidth called the Mizuno limit or peak sensitivitybandwidth product [11] which applies in general to quantum position measurement devices using a resonant cavity [12][13][14]. This arises due to the positive dispersion of the arm cavities: when the sideband frequency is near zero the light is resonantly enhanced by constructive interference, however as the sideband frequency is increased the light begins to destructively interfere.…”

Quantum Limit for Laser Interferometric Gravitational-Wave Detectors from Optical Dissipation

“…As shown in Ref. [16], the QCRB can be approached in a lossless systems with optimal frequency-dependent homodyne readout, which can be realized with proper output filters [9]. This result has been generalised to laser interferometers with multiple carrier frequencies [17].…”