Quantum sensing utilizing unique quantum properties of non-Hermitian systems to realize ultra-precision measurements has been attracting increasing attention. However, the debate on whether non-Hermitian systems are superior to Hermitian counterparts in sensing remains an open question. Here, we investigate the quantum information in PT-symmetric quantum sensing utilizing two experimental schemes based on the trapped-ion platform. It turns out that the existence of advantages of non-Hermitian quantum sensing heavily depends on additional information resources carried by the extra degrees of freedom introduced to construct PT-symmetric quantum sensors. Moreover, the practical application of non-Hermitian quantum sensing with superior performance is primarily restricted by the additional resource consumption accompanied by the post-selection. Our study provides theoretical references for the construction of non-Hermitian quantum sensors with superior performance and has potential applications in research fields of quantum precision measurement and quantum information processing.
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.
Unconventional properties of non-Hermitian systems, such exceptional points, have recently been suggested as a resource for sensing. The impact of noise and utility in quantum regimes, however, remain highly debatable. In this talk, I will introduce a full theoretical framework to analyze the performance of a dispersive quantum non-Hermitian sensor; parts of our result have been included in our recent paper Lau & Clerk, Nat. Comm. 9, 4320 (2018). Our formalism fully accounts for noise effects in both classical and quantum regimes, and also fully treats a realistic and optimal measurement protocol based on coherent driving and homodyne detection. Focusing on two-mode devices, we derive fundamental bounds on the signal-to-noise (SNR) ratio for any such sensor. We use these to demonstrate that enhanced SNR ratio does not necessarily require any proximity to an exceptional point. Furthermore, we show that non-reciprocity is a powerful resource for sensing even when quantum noise exists.
In recent years, non-Hermitian parity-time (
PT)-symmetric quantum systems have gained significant attention due to their unique physical properties, with experimental realizations demonstrated across diverse platforms. Two popular approaches have been used to implement
PT-symmetric dynamics: one removes quantum jumps from dissipative natural atoms (e.g., cold atoms, trapped ions) or artificial atoms (e.g., superconducting qubits) through postselection whose experimental fidelity is severely limited by unavoidable population backflow effects; the other embeds the desired non-Hermitian Hamiltonian into a larger Hermitian system, which achieves higher fidelity but typically enables simulating
PT-symmetric dynamics only within restricted parameter regimes. This paper proposes and experimentally demonstrates a trapped-ion-based scheme for digital simulation of
PT-symmetric quantum systems with high fidelity across the full parameter space. By leveraging high-fidelity logic gates and postselection on a four-level single ion to synthesize the target
PT-symmetric dynamics, this approach enables accurate characterization of
PT-symmetric properties, especially the exotic features in the vicinity of the exceptional point (EP). Distinct dynamical properties in the
PT-symmetric unbroken phase (PTS),
PT-symmetric broken phase (PTB), and at the EP are experimentally demonstrated with the data agreeing well with theoretical predictions. This high-fidelity simulation scheme also enables precise measurement of quantum Fisher information (QFI) near the EP, essential for evaluating non-Hermitian quantum sensing performance. It is shown that, after accounting for the low postselection probability, QFI divergence near the EP vanishes, providing no more information than their Hermitian counterparts, which echoes with recent theoretical findings. Our scheme establishes a paradigm for full-parameter-space precise simulation of non-Hermitian effects in quantum systems, and is applicable to various other platforms.
By employing the Naimark dilation, we establish a fundamental connection between non-Hermitian quantum sensing and postselected measurements. The sensitivity of non-Hermitian quantum sensors is determined by the effective quantum Fisher information (QFI), which incorporates the success probability of postselection. We demonstrate that non-Hermitian sensors, regardless of the specific form of decoherence or the choice of probe states, cannot outperform their Hermitian counterpart when all information is harnessed, since the total QFI for the extended system constrains the effective QFI of the non-Hermitian subsystem. Moreover, we quantify the efficiency of non-Hermitian sensors with the ratio of the effective QFI to the total QFI, which can be optimized within the framework of postselected measurements with minimal experimental trials. In addition, the performances of non-Hermitian sensors versus different types of technical noises can be judged using our framework. Our work provides a distinctive theoretical framework for investigating non-Hermitian quantum sensing and designing noise-resilient quantum metrological protocols.
Considering non-Hermitian systems implemented by utilizing enlarged quantum systems, we determine the fundamental limits for the sensitivity of non-Hermitian sensors from the perspective of quantum information. We prove that non-Hermitian sensors do not outperform their Hermitian counterparts (directly couple to the parameter) in the performance of sensitivity, due to the invariance of the quantum information about the parameter. By scrutinizing two concrete non-Hermitian sensing proposals, which are implemented using full quantum systems, we demonstrate that the sensitivity of these sensors is in agreement with our predictions. Our theory offers a comprehensive and model-independent framework for understanding the fundamental limits of non-Hermitian quantum sensors and builds the bridge over the gap between non-Hermitian physics and quantum metrology.