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Nonlinear Enhancement of Measurement Precision via a Hybrid Quantum Switch

Chuan‐Feng Li, Lei Chen, Yuxiang Yang, Gongchu Li, Xu-Song hong, Siqi Zhang, H. Xu, Yuan-Cheng Liu, Giulio Chiribella, Geng Chen, Guang-Can Guo

Published Oct 18, 2024• 0 citations
Publisher

Abstract

Abstract Quantum metrology promises measurement precision beyond the classical limit by using suitably tailored quantum states and detection strategies. However, scaling up this advantage is experimentally challenging, due to the difficulty of generating high-quality large-scale probes. Here, we build a photonic setup that achieves enhanced precision scaling by manipulating the probe’s dynamics through operations performed in a coherently controlled order. Our setup applies an unknown rotation and a known orbital angular momentum increase in a coherently controlled order, in a way that reproduces a hybrid quantum SWITCH involving gates generated by both discrete and continuous variables. The unknown rotation angle θ is measured with precision scaling as 1/4ml when a photon undergoes a rotation of 2mθ and an angular momentum shift of 2lℏ. With a practical enhancement factor as high as 2317, the ultimate precision in our experiment is 0.0105′′ when using 7.16 × 107 photons, corresponding to a normalized precision of ≈ 10−4rad per photon. No photon interaction occurs in our experiment, and the precision enhancement consumes only a linearly increasing amount of physical resources while achieving a nonlinear scaling of the precision.

DOI
10.21203/rs.3.rs-4969442/v1

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Abstract Quantum metrology promises measurement precision beyond the classical limit by using suitably tailored quantum states and detection strategies. However, scaling up this advantage is experimentally challenging, due to the difficulty of generating high-quality large-scale probes. Here, we build a photonic setup that achieves enhanced precision scaling by manipulating the probe’s dynamics through operations performed in a coherently controlled order. Our setup applies an unknown rotation and a known orbital angular momentum increase in a coherently controlled order, in a way that reproduces a hybrid quantum SWITCH involving gates generated by both discrete and continuous variables. The unknown rotation angle θ is measured with precision scaling as 1/4ml when a photon undergoes a rotation of 2mθ and an angular momentum shift of 2lℏ. With a practical enhancement factor as high as 2317, the ultimate precision in our experiment is 0.0105′′ when using 7.16 × 107 photons, corresponding to a normalized precision of ≈ 10−4rad per photon. No photon interaction occurs in our experiment, and the precision enhancement consumes only a linearly increasing amount of physical resources while achieving a nonlinear scaling of the precision.
Quantum metrology promises measurement precision beyond the classical limit by using suitably tailored quantum states and detection strategies. However, scaling up this advantage is experimentally challenging, due to the difficulty of generating high-quality large-scale probes. Here, we build a photonic setup that achieves enhanced precision scaling by manipulating the probe's dynamics through operations performed in a coherently controlled order. Our setup applies an unknown rotation and a known orbital angular momentum increase in a coherently controlled order, in a way that reproduces a hybrid quantum SWITCH involving gates generated by both discrete and continuous variables. The unknown rotation angle θθθ is measured with precision scaling as 1/4ml1/4ml1/4ml when a photon undergoes a rotation of 2mθ2mθ2mθ and an angular momentum shift of 2lℏ2l \hbar2lℏ. With a practical enhancement factor as high as 2317, the ultimate precision in our experiment is 0.0105′′0.0105^{\prime \prime}0.0105′′ when using 7.16×1077.16\times10^77.16×107 photons, corresponding to a normalized precision of ≈10−4\approx 10^{-4}≈10−4rad per photon. No photon interaction occurs in our experiment, and the precision enhancement consumes only a linearly increasing amount of physical resources while achieving a nonlinear scaling of the precision. We further indicate that this nonlinear enhancement roots in an in-depth exploration of the Heisenberg uncertainty principle (HUP), and our findings not only deepen the understanding of the HUP but also pave a pathway for advancements in quantum metrology.
The precision limit in quantum metrology, quantified by the root-mean-square error of parameter estimation, is conventionally expected to improve at most linearly with the total interrogation time T and with the number N of queried quantum gates. Although several metrological schemes have been shown to achieve precision scaling faster than linear in T and N, they typically rely on unbounded probe-side information resources, usually qualified by an increasingly large variance of the parameter generator. This requirement complicates the interpretation of the resulting scaling advantage and poses substantial technical challenges. In this work, we employ an indefinite-time-direction encoding process to achieve a nonlinear-scaling enhancement of the precision limit. Rather than relying on increasingly informative probe states, our method converts controllable noncommuting encoding operations into metrological gain. Experimentally, we implement this protocol for angular-rotation measurement in a quantum optical system and demonstrate a nonlinear-scaling improvement in practical precision without using probe-side information resources. These results establish a practical framework for surpassing conventional linear-scaling precision limits in quantum metrology and provide new insights into precision enhancement in realistic quantum metrological and sensing applications.
Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.
Abstract This study demonstrates that quantum switch can be applied to an entangled system comprising a control qubit and a probe state for parameter estimation, providing additional resources and degrees of freedom to enhance precision. Using a photon probe state as an example, we show that while this approach does not surpass the Heisenberg scaling, it can exceed the Heisenberg bound compared to a definite causal order scheme. For the quantum harmonic oscillator state, when the product of its mass and angular frequency mω is extremely large or extremely small, a suitable encoding method can always be selected to improve the precision. Finally, we demonstrate that if certain operators with specific commutation relations can be realized, the measurement precision has the potential to be further improved.
Abstract Adopting quantum resources for parameter estimation discloses the possibility to realize quantum sensors operating at a sensitivity beyond the standard quantum limit. Such an approach promises to reach the fundamental Heisenberg scaling as a function of the employed resources N in the estimation process. Although previous experiments demonstrated precision scaling approaching Heisenberg-limited performances, reaching such a regime for a wide range of N remains hard to accomplish. Here, we show a method that suitably allocates the available resources permitting them to reach the same power law of Heisenberg scaling without any prior information on the parameter. We demonstrate experimentally such an advantage in measuring a rotation angle. We quantitatively verify sub-standard quantum limit performances for a considerable range of N (O(30,000)) by using single-photon states with high-order orbital angular momentum, achieving an error reduction, in terms of the obtained variance, >10 dB below the standard quantum limit. Such results can be applied to different scenarios, opening the way to the optimization of resources in quantum sensing.
We propose a high-precision phase estimation scheme in a hybrid interferometer by synergistically combining a Kerr nonlinear phase shifter and multi-photon subtraction operations. Using a coherent state and a vacuum state as input resources, we systematically evaluate the phase sensitivity via homodyne detection and analyze the quantum Fisher information as well as the quantum Cramér-Rao bound under both ideal and lossy conditions. Our results show that the joint integration of Kerr nonlinearity and multi-photon subtraction yields remarkable advantages over either technique used alone. The proposed scheme enables the phase sensitivity to surpass the standard quantum limit, exceed the conventional Heisenberg scaling (1/N1/N1/N), and approach the super-Heisenberg scaling (1/N21/N^{2}1/N2)-a direct consequence of Kerr nonlinearity. More precisely, the super-Heisenberg scaling $\propto $ 1/N21/N^{2}1/N2 is the ultimate precision limit permitted by the k=2k=2k=2 Kerr nonlinearity and does not violate the fundamental Heisenberg limit for linear phase accumulation. Even under moderate internal photon loss, the system maintains high precision and exhibits enhanced robustness to decoherence. The Kerr nonlinearity introduces an intensity-dependent phase shift proportional to the squared photon number, while multi-photon subtraction tailors non-Gaussian states to strengthen phase information extraction. Compared with existing schemes based on hybrid interferometers or SU(1,1) interferometers, our architecture achieves superior precision and stronger loss resilience. All components are experimentally accessible with current quantum optical technologies. This work provides a promising route for practical high-precision quantum metrology and quantum sensing.