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Communications in Theoretical Physics

Prefect Protection of Quantum-Enhanced Metrology from Dephasing Noise*

Wei Zhong, Yixiao Huang, Xiaoguang Wang

Published Apr 1, 2017• 1 citation
Publisher

Abstract

Abstract One of the main obstacles for quantum-enhanced metrology is that the estimation accuracy enhanced by non-classical states is likely to be obliterated by noises. Here, we consider a scenario of phase estimation suffering from pure dephasing noise which is taken into account after the phase parameter being imprinted, and propose a scheme to effectively protect the quantum enhancement from both correlated and uncorrelated dephasing sources by performing a rotation operation prior to the noise. By invoking the Fisher information approach, we strictly prove that a π / 2 rotation is the ideal one which can completely resist the influence of the phase noise for all real symmetric pure states and the optimal measurement approaching the ultimate sensitivity set by quantum Cramér–Rao bound is presented. Additionally, we numerically study the availability of the scheme with arbitrary angle rotation for different probe states and show that our scheme will still robust for general symmetric pure states even with non-ideal rotation operation.

DOI
10.1088/0253-6102/67/4/383

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Abstract One of the main obstacles for quantum-enhanced metrology is that the estimation accuracy enhanced by non-classical states is likely to be obliterated by noises. Here, we consider a scenario of phase estimation suffering from pure dephasing noise which is taken into account after the phase parameter being imprinted, and propose a scheme to effectively protect the quantum enhancement from both correlated and uncorrelated dephasing sources by performing a rotation operation prior to the noise. By invoking the Fisher information approach, we strictly prove that a π / 2 rotation is the ideal one which can completely resist the influence of the phase noise for all real symmetric pure states and the optimal measurement approaching the ultimate sensitivity set by quantum Cramér–Rao bound is presented. Additionally, we numerically study the availability of the scheme with arbitrary angle rotation for different probe states and show that our scheme will still robust for general symmetric pure states even with non-ideal rotation operation.
We exploit the theory of quantum estimation to investigate quantum state estimation in the presence of noise. The quantum Fisher information is used to assess the estimation performance. For the qubit in Bloch representation, general expressions are derived for the quantum score and then for the quantum Fisher information. From this latter expression, it is proved that the Fisher information always increases with the purity of the measured qubit state. An arbitrary quantum noise affecting the qubit is taken into account for its impact on the Fisher information. The task is then specified to estimating the phase of a qubit in a rotation around an arbitrary axis, equivalent to estimating the phase of an arbitrary single-qubit quantum gate. The analysis enables determination of the optimal probing states best resistant to the noise, and proves that they always are pure states but need to be specifically matched to the noise. This optimization is worked out for several noise models important to the qubit. An adaptive scheme and a Bayesian approach are presented to handle phase-dependent solutions.
We examine metrological scenarios where the parameter of interest is encoded onto a quantum state through the action of a noisy quantum gate and investigate the ultimate bound to precision by analyzing the behavior of the quantum Fisher information (QFI). We focus on qubit gates and consider the possibility of employing successive applications of the gate. We go beyond the trivial case of unitary gates and characterize the robustness of the metrological procedure introducing noise in the performed quantum operation, looking at how this affects the QFI at different steps (gate applications). We model the dephasing and tilting noise affecting qubit rotations as classical fluctuations governed by a von Mises--Fisher distribution. Compared to the noiseless case, in which the QFI grows quadratically with the number of steps, we observe a nonmonotonic behavior, and the appearance of a maximum in the QFI, which defines the ideal number of steps that should be performed in order to precisely characterize the action of the gate. Analyzing also the combination of different types of gate imperfections we defined a form of generic noise, finding also nontrivial regimes in which the combination of the two different noises leads to a more resilient QFI or, more remarkably, to an enhancement of the QFI with respect to the case in which only one type of noise is considered.
The quantum Fisher information and quantum correlation parameters are employed to study the application of nonclassical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state is determined by its intermode correlations (which depends on path entanglement) and intramode correlations (which depends on the photon statistics). In light of these results, we consider the performance of quantum-enhanced optical interferometers. Furthermore, we propose a Heisenberg-limited metrology protocol involving standard elements from passive and active linear optics, for which the quantum Cram\'er-Rao bound is saturated with an intensity measurement. Interestingly, the quantum advantage for this scheme is derived solely from the nonclassical photon statistics of the probe state and does not depend on entanglement. We study the performance of this scheme in the presence of realistic losses and consequently predict a substantial enhancement over the shot-noise limit with current technological capabilities.
The goal of quantum metrology is the precise estimation of parameters using quantum properties such as entanglement. This estimation usually consists of three steps: state preparation, time evolution during which information of the parameters is encoded in the state, and readout of the state. Decoherence during the time evolution typically degrades the performance of quantum metrology and is considered to be one of the major obstacles to realizing entanglement-enhanced sensing. We show, however, that under suitable conditions, this decoherence can be exploited to improve the sensitivity. Assume that we have two axes, and our aim is to estimate the relative angle between them. Our results reveal that the use of Markovian collective dephasing to estimate the relative angle between the two directions affords Heisenberg-limited sensitivity. Moreover, our protocol based on Markovian collective dephasing is robust against environmental noise: it is possible to achieve the Heisenberg limit by applying the collective dephasing even under the effect of independent dephasing. Our counterintuitive proposal with the decoherence leads to alternative applications in quantum metrology.
Quantum-enhanced interferometers utilize non-classical states of light in order to surpass the limitations imposed by classical physics on phase measurement sensitivity and resolution. We review key scientific developments in this growing field of research and derive fundamental metrology concepts, namely the Cram\'{e}r-Rao bound and the Fisher information, which are used to analyze the metrological performance of quantum states of light. We propose a supersensitive quantum interferometry protocol that can be amplified to the macroscopic realm (i.e. the mean number of photons of the probe state can reach approximately 100,000 photons) using contemporary techniques of spontaneous parametric down conversion. The parity measurement on the output field asymptotically saturates the quantum Cram\'{e}r-Rao bound, which scales like the Heisenberg limit. We uncover the role of photon statistics on phase sensitivity and rule out the necessity of mode entanglement for quantum-enhanced interferometry. Based on these insights we outline a practical metrology technique (independent of mode entanglement) that measures a phase delay of a single-mode anti-squeezing operation. This scheme can also be scaled macroscopically using contemporary techniques and is shown to significantly surpass the shot-noise limit (SNL) in the presence of realistic losses. Finally, the physical resources that enable quantum-enhanced interferometry is studied by analyzing the quantum Fisher information (QFI) using the first quantization and the second quantization formalisms of quantum mechanics. It is shown that increasing the intra-mode correlations of an interferometer (as quantified by the second order Glauber coherence function) can be conducive to attaining a quantum advantage in phase estimation; whereas, introducing mode entanglement can reduce phase sensitivity. Using the first quantization description, we derive a formula for the QFI that shows explicitly how the Heisenberg scaling term depends on particle entanglement.
While quantum metrology enables measurement precision beyond classical limits, its performance is often susceptible to experimental imperfections. Most prior studies have focused on imperfections in quantum states and operations. Here, we investigate the effect of coarse graining in quantum measurement through both theoretical analysis and experimental demonstration. Using an interferometer with a squeezed vacuum and a laser input, we analyze how coarse graining in homodyne detection affects the precision of phase estimation. We evaluate the Fisher information under various coarse-graining conditions and determine, in each case, an optimal estimation strategy that saturates the Cramér-Rao bound. Remarkably, even extremely coarse-grained measurement -- with only two bins -- enables phase estimation beyond the standard quantum limit and even achieves a precision that follows the Heisenberg scaling. We experimentally demonstrate quantum-enhanced phase estimation under coarse-grained homodyne detection. To determine an optimal estimation strategy, we employ the method of moments and present calibration procedures that enable its application to general experimental settings. Using only two bins, we observe a quantum enhancement of 1.2 dB compared to the classical method using the ideal measurement, improving towards 3.8 dB as the bin number increases. These results highlight a practical pathway to achieving quantum enhancement under the presence of severe experimental imperfections.