Abstract
This paper studies quantum limits to dynamical sensors in the presence of decoherence. A modified purification approach is used to obtain tighter quantum detection and estimation error bounds for optical phase sensing and optomechanical force sensing. When optical loss is present, these bounds are found to obey shot-noise scalings for arbitrary quantum states of light under certain realistic conditions, thus ruling out the possibility of asymptotic Heisenberg error scalings with respect to the average photon flux under those conditions. The proposed bounds are expected to be approachable using current quantum optics technology.
Highlights
The laws of quantum mechanics impose fundamental limitations to the accuracy of measurements, and a fundamental question in quantum measurement theory is how such limitations affect precision sensing applications, such as gravitational-wave detection, optical interferometry, and atomic magnetometry and gyroscopy [1, 2]
A quantum Cramer-Rao bound (QCRB) for waveform estimation [10] and a quantum fidelity bound for waveform detection [11] have recently been proved, generalizing earlier seminal results by Helstrom [12]
(iii) A quantum model of optomechanical force sensing can be transformed to an optical phase sensing problem with classical phase shift, such that a unified formalism can treat both problems and produce tighter bounds than the results in [10, 11]
Summary
The laws of quantum mechanics impose fundamental limitations to the accuracy of measurements, and a fundamental question in quantum measurement theory is how such limitations affect precision sensing applications, such as gravitational-wave detection, optical interferometry, and atomic magnetometry and gyroscopy [1, 2]. With the rapid recent advance in quantum optomechanics [3,4,5,6,7] and atomic [8,9] technologies, quantum sensing limits have received renewed interest and are expected to play a key role in future precision measurement applications Many realistic sensors, such as gravitational-wave detectors, perform continuous measurements of time-varying signals (commonly called waveforms). (iii) A quantum model of optomechanical force sensing can be transformed to an optical phase sensing problem with classical phase shift, such that a unified formalism can treat both problems and produce tighter bounds than the results in [10, 11] These results provide more general and realistic quantum limits that can be approached using current quantum optics technology [31,32,33,34,35,36], but may be relevant to more general studies of quantum metrology and quantum information, such as quantum speed limits [37, 38] and Loschmidt echo [39]
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