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arXiv:2408.02282 · Communications Physics

Enhanced quantum hypothesis testing via the interplay between coherent evolution and noises

Qing Li, Lingna Wang, Min Jiang, Ze Wu, Haidong Yuan, Xinhua Peng

Published Jan 14, 2025• 0 citations
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Abstract

Previous studies in quantum information have recognized that specific types of noise can encode information in certain applications. However, the role of noise in quantum hypothesis testing, traditionally assumed to undermine performance, has not been thoroughly explored. Our study provides sufficient conditions for general noisy dynamics to surpass noiseless (unitary) dynamics within certain time interval. We then design and experimentally implement a noise-assisted quantum hypothesis testing protocol on ultralow-field nuclear magnetic resonance systems, which demonstrates that the success probability under certain noisy dynamics can indeed surpass the ceiling set by unitary evolution. Moreover, we show that in cases where noise initially hampers performance, strategic application of coherent controls on the system can transform those previously detrimental noises into advantageous ones. Our results, both theoretical and experimental, demonstrates the potential to leveraging noise in quantum hypothesis testing, which pushes the boundaries of quantum hypothesis testing and general quantum information processing. In quantum science, quantum hypothesis testing (QHT) is used to determine the model of a given quantum system, but normally the presence of inherent quantum noise hampers perfect hypothesis testing. The authors theoretically and experimentally explore the potential of leveraging noise in quantum hypothesis testing (QHT) to surpass the success probabilities achievable under noiseless dynamics.

DOI
10.1038/s42005-024-01923-z

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Previous studies in quantum information have recognized that specific types of noise can encode information in certain applications. However, the role of noise in quantum hypothesis testing, traditionally assumed to undermine performance, has not been thoroughly explored. Our study provides sufficient conditions for general noisy dynamics to surpass noiseless (unitary) dynamics within certain time interval. We then design and experimentally implement a noise-assisted quantum hypothesis testing protocol on ultralow-field nuclear magnetic resonance systems, which demonstrates that the success probability under certain noisy dynamics can indeed surpass the ceiling set by unitary evolution. Moreover, we show that in cases where noise initially hampers performance, strategic application of coherent controls on the system can transform those previously detrimental noises into advantageous ones. Our results, both theoretical and experimental, demonstrates the potential to leveraging noise in quantum hypothesis testing, which pushes the boundaries of quantum hypothesis testing and general quantum information processing. In quantum science, quantum hypothesis testing (QHT) is used to determine the model of a given quantum system, but normally the presence of inherent quantum noise hampers perfect hypothesis testing. The authors theoretically and experimentally explore the potential of leveraging noise in quantum hypothesis testing (QHT) to surpass the success probabilities achievable under noiseless dynamics.
The primary challenge in advancing practical quantum technology is the presence of noise, which can lead to decoherence and undermine the advantages of quantum systems. However, it is worth noting that noise can also contain information that can be harnessed to improve performance in certain quantum information tasks. This has been explored for specific types of noise, but the full potential of informative noise within general dynamics remains largely unknown. Here we demonstrate that informative noise can be transformed into a valuable resource for enhancing precision limits in quantum metrology. We provide necessary and sufficient conditions under which the precision achieved in the presence of informative noise can attain Heisenberg scaling. Our research offers a fresh perspective on the role of noise in quantum metrology and opens up avenues for achieving higher precision beyond the previously anticipated ultimate limit.
Non-Hermitian systems have emerged as a powerful paradigm for ultrasensitive sensing, leveraging unique spectral and dynamical properties unmatched in Hermitian physics. While recent theoretical bounds suggest these protocols offer no metrological advantage over Hermitian ones in the ideal shot-noise-limited regime when rigorously accounting for the success probability of non-unitary evolution, their practical utility in realistic experimental conditions has not yet been systematically explored. In this work, we shift the focus toward practical laboratory performance and demonstrate that non-Hermitian sensing protocols can significantly outperform their Hermitian counterparts in the presence of pervasive classical technical noises. This performance gain mainly stems from a strongly enhanced susceptibility that amplifies the signal response, effectively overcoming the precision floor imposed by technical imperfections. By numerically evaluating the Fisher information under technical noise, we further substantiate the regimes where non-Hermitian platforms yield definitive practical gains. Our results reconcile the ongoing debate between fundamental limits and experimental observations, offering a concrete avenue for building high-precision, noise-resilient sensors.
Abstract Quantum hypothesis testing plays a pivotal role in quantum technologies, making decisions or drawing conclusions about quantum systems based on observed data. Recently, quantum control techniques have been successfully applied to quantum hypothesis testing, enabling the reduction of error probabilities in the task of distinguishing magnetic fields in presence of environmental noise. In real-world physical systems, such control is prone to various channels of inaccuracies. Therefore improving the robustness of quantum control in the context of quantum hypothesis testing is crucial. In this work, we utilize optimal control methods to compare scenarios with and without accounting for the effects of signal frequency inaccuracies. For parallel dephasing and spontaneous emission, the optimal control inherently demonstrates a certain level of robustness, while in the case of transverse dephasing with an imperfect signal, it may result in a higher error probability compared to the uncontrolled scheme. To overcome these limitations, we introduce a robust control approach optimized for a range of signal noise, demonstrating superior robustness beyond the predefined tolerance window. On average, both the optimal control and robust control show improvements over the uncontrolled schemes for various dephasing or decay rates, with the robust control yielding the lowest error probability.
Quantum Zeno dynamics (QZD), which restricts the system's evolution to a protected subspace, provides a promising approach for protecting quantum information from noise. Here, we explore a practical approach to harnessing QZD for robust quantum metrology. By introducing strong inter-particle interactions during the parameter encoding stage, we overcome the typical limitations of previous QZD studies, which have largely focused on single-particle systems and faced challenges where QZD could interfere with the encoding process. We experimentally validate the proposed scheme on a nuclear magnetic resonance platform, achieving near-optimal precision scaling under amplitude damping in both parallel and sequential settings. Numerical simulations further demonstrate the scalability of the approach and its compatibility with other control techniques for suppressing more general types of noise. These findings highlight QZD as a powerful strategy for noise-resilient quantum metrology.
Quantum metrology promises unprecedented precision of parameter estimation, but it is often vulnerable to noise. While significant efforts have been devoted to improving the metrology performance in Markovian environments, practical control schemes specifically designed for non-Markovian noises are much less investigated. Here, we propose two control-enhanced quantum metrology schemes that are suitable for tackling general non-Markovian noises described by noise channels or noise spectra. We conduct experiments to verify the efficacy of these schemes on a nuclear magnetic resonance system. The experimental results involving multiqubit probes show that the parameter estimation precision can be greatly improved, significantly surpassing the standard quantum limit, with our schemes. At present, non-Markovian noises are widely encountered on diverse quantum devices, the proposed schemes are relevant for realistic metrology applications on these platforms. Quantum metrology, a powerful paradigm for surpassing classical measurement precision, has been extensively studied for Markovian noise, while most practical physical processes obey non-Markovian dynamics. In this paper, the authors propose control-enhanced quantum metrology schemes to counteract non-Markovian noise and experimentally verify their efficacy.
Quantum hypothesis testing (QHT) concerns the statistical inference of unknown quantum states. In the general setting of composite hypotheses, the goal of QHT is to determine whether an unknown quantum state belongs to one or another of two classes of states based on the measurement of a number of copies of the state. Prior art on QHT with composite hypotheses focused on a fixed-copy two-step protocol, with state estimation followed by an optimized joint measurement. However, this fixed-copy approach may be inefficient, using the same number of copies irrespective of the inherent difficulty of the testing task. To address these limitations, we introduce the quantum sequential universal test (QSUT), a novel framework for sequential QHT in the general case of composite hypotheses. QSUT builds on universal inference, and it alternates between adaptive local measurements aimed at exploring the hypothesis space and joint measurements optimized for maximal discrimination. QSUT is proven to rigorously control the type I error under minimal assumptions about the hypothesis structure. We present two practical instantiations of QSUT, one based on the Helstrom-Holevo test and one leveraging shallow variational quantum circuits. Empirical results across a range of composite QHT tasks demonstrate that QSUT consistently reduces copy complexity relative to state-of-the-art fixed-copy strategies.