Quantum metrology, such as quantum phase estimation, can surpass classical sensing limits, reaching the Heisenberg‐scaling precision. So far, this kind of metrology has been thought to be only implementable with the quantum systems, which, however, are fragile to environmental noise and hardly contribute to the practical detections. Herein, it is demonstrated both theoretically and experimentally that the parameter encoded by the optical phase can also be estimated at the Heisenberg scaling in classical optics. Inspired by the quantum‐entanglement‐enhanced sensing scheme, the estimation is performed by using classically correlated beams as probes, and obtaining the probes readout after their interaction with the target system. Because the correlated beams considered are spatially separable, a distributed phase estimation scheme is given, which can sense the linear combinations of the phase shifts induced by distinct systems. The results of our experiments show an error reduction up to 3.89 dB below the classical limit when the correlated beam number for probing is 6, approaching the Heisenberg limit. Compared with quantum strategies, the proposal shows a better robustness against the environmental disturbance and keeps their performances even when the correlated beam number is relatively large. Hence, it indicates promising practical applications in the future.Quantum metrology, such as quantum phase estimation, can surpass classical sensing limits, reaching the Heisenberg‐scaling precision. So far, this kind of metrology has been thought to be only implementable with the quantum systems, which, however, are fragile to environmental noise and hardly contribute to the practical detections. Herein, it is demonstrated both theoretically and experimentally that the parameter encoded by the optical phase can also be estimated at the Heisenberg scaling in classical optics. Inspired by the quantum‐entanglement‐enhanced sensing scheme, the estimation is performed by using classically correlated beams as probes, and obtaining the probes readout after their interaction with the target system. Because the correlated beams considered are spatially separable, a distributed phase estimation scheme is given, which can sense the linear combinations of the phase shifts induced by distinct systems. The results of our experiments show an error reduction up to 3.89 dB below the classical limit when the correlated beam number for probing is 6, approaching the Heisenberg limit. Compared with quantum strategies, the proposal shows a better robustness against the environmental disturbance and keeps their performances even when the correlated beam number is relatively large. Hence, it indicates promising practical applications in the future.

Advanced Photonics ResearchDec 20, 20233 citations

Phase detection at the quantum limit

Juan F. Hodelin, Luca Pezzè, G. Khoury +2 more

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEJan 1, 20080 citations

Sensing past the quantum limit

Christopher G. Baker, Warwick P. Bowen

NatureJul 1, 20172 citations

Asymptotic role of entanglement in quantum metrology

Remigiusz Augusiak, Jan Kołodyński, Alexander Streltsov +3 more

Quantum systems allow one to sense physical parameters beyond the reach of classical statistics---with resolutions greater than $1/N$ , where $N$ is the number of constituent particles independently probing a parameter. In the canonical phase-sensing scenario the Heisenberg limit $1/{N}^{2}$ may be reached, which requires, as we show, both the relative size of the largest entangled block and the geometric measure of entanglement to be nonvanishing as $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Yet, we also demonstrate that in the asymptotic $N$ limit any precision scaling arbitrarily close to the Heisenberg limit ($1/{N}^{2\ensuremath{-}\ensuremath{\varepsilon}}$ with any $\ensuremath{\varepsilon}>0$) may be attained, even though the system gradually becomes noisier and separable, so that both the above entanglement quantifiers asymptotically vanish. Our work shows that sufficiently large quantum systems achieve nearly optimal resolutions despite their relative amount of entanglement being arbitrarily small. In deriving our results, we establish the continuity relation of the quantum Fisher information evaluated for a phaselike parameter, which lets us link it directly to the geometry of quantum states, and hence naturally to the geometric measure of entanglement.Quantum systems allow one to sense physical parameters beyond the reach of classical statistics---with resolutions greater than $1/N$, where $N$ is the number of constituent particles independently probing a parameter. In the canonical phase-sensing scenario the Heisenberg limit $1/{N}^{2}$ may be reached, which requires, as we show, both the relative size of the largest entangled block and the geometric measure of entanglement to be nonvanishing as $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Yet, we also demonstrate that in the asymptotic $N$ limit any precision scaling arbitrarily close to the Heisenberg limit ($1/{N}^{2\ensuremath{-}\ensuremath{\varepsilon}}$ with any $\ensuremath{\varepsilon}>0$) may be attained, even though the system gradually becomes noisier and separable, so that both the above entanglement quantifiers asymptotically vanish. Our work shows that sufficiently large quantum systems achieve nearly optimal resolutions despite their relative amount of entanglement being arbitrarily small. In deriving our results, we establish the continuity relation of the quantum Fisher information evaluated for a phaselike parameter, which lets us link it directly to the geometry of quantum states, and hence naturally to the geometric measure of entanglement.

arXiv:1506.08837Physical Review AJul 22, 201645 citations

Quantum Speed Limit in Quantum Sensing

Konstantin Herb, Christian L. Degen

Quantum sensors capitalize on advanced control sequences for maximizing sensitivity and precision. However, protocols are not usually optimized for temporal resolution. Here, we establish the limits for time-resolved sensing of dynamical signals using qubit probes. We show that the best possible time resolution is closely related to the quantum speed limit (QSL), which describes the minimum time needed to transform between basis states. We further show that a composite control sequence consisting of two phase-shifted pulses reaches the QSL. Practical implementation is discussed based on the example of the spin-1 qutrit of a nitrogen-vacancy center in diamond.Quantum sensors capitalize on advanced control sequences for maximizing sensitivity and precision. However, protocols are not usually optimized for temporal resolution. Here, we establish the limits for time-resolved sensing of dynamical signals using qubit probes. We show that the best possible time resolution is closely related to the quantum speed limit (QSL), which describes the minimum time needed to transform between basis states. We further show that a composite control sequence consisting of two phase-shifted pulses reaches the QSL. Practical implementation is discussed based on the example of the spin-1 qutrit of a nitrogen-vacancy center in diamond.

arXiv:2406.18348Physical Review LettersNov 19, 202420 citations

Phase-Sensitive Quantum Spectroscopy

Daniel F. Walls, M. D. Reid, P. Zoller +1 more

Springer series in optical sciences/SPringer series in optical sciencesJan 1, 19850 citations

Quantum systems allow one to sense physical parameters beyond the reach of classical statistics---with resolutions greater than

1/N

, where

N

is the number of constituent particles independently probing a parameter. In the canonical phase-sensing scenario the Heisenberg limit

1/{N}^{2}

may be reached, which requires, as we show, both the relative size of the largest entangled block and the geometric measure of entanglement to be nonvanishing as $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Yet, we also demonstrate that in the asymptotic

N

limit any precision scaling arbitrarily close to the Heisenberg limit ($1/{N}^{2\ensuremath{-}\ensuremath{\varepsilon}}$ with any $\ensuremath{\varepsilon}>0$) may be attained, even though the system gradually becomes noisier and separable, so that both the above entanglement quantifiers asymptotically vanish. Our work shows that sufficiently large quantum systems achieve nearly optimal resolutions despite their relative amount of entanglement being arbitrarily small. In deriving our results, we establish the continuity relation of the quantum Fisher information evaluated for a phaselike parameter, which lets us link it directly to the geometry of quantum states, and hence naturally to the geometric measure of entanglement.