Practical advantage of non-Hermitian enhanced quantum sensing

Abstract

Non-Hermitian systems have emerged as a powerful paradigm for ultrasensitive sensing, leveraging unique spectral and dynamical properties that find no counterparts in Hermitian physics. While recent theoretical assessments have established that these protocols offer no fundamental advantage in the ideal shot-noise-limited regime once the success probability of non-unitary evolution is rigorously accounted for, their practical utility under realistic experimental constraints remains largely unexplored. In this work, we shift the focus toward practical laboratory performance by demonstrating that non-Hermitian sensors can significantly outperform their Hermitian counterparts in the presence of various types of technical noise. This enhancement stems from the significantly enhanced susceptibility, which amplifies the signal response to effectively overcome the floor of technical imperfections. By evaluating the Fisher information under different technical noise models, we further substantiate the superior performance of non-Hermitian sensing. Our results delineate the specific regimes where non-Hermitian platforms yield clear practical gains, offering a concrete avenue for building high-precision, noise-resilient sensors.

Figures (8)

• Figure 1: Relationship of the susceptibility $\chi_\lambda$ with the control parameter $\delta$. When $|\mathcal{D}_t|\sim|\delta|\ll 1$, the non-Hermitian system exhibits a sharply divergent response as $|\delta|\rightarrow 0$, which is much more prominent than the corresponding Hermitian evolution.
• Figure 2: Statistics of quantum measurement outcomes and biased readout error. Histograms of detected photon counts or the qubit prepared in the $| 0 \rangle$ (blue) and $| 1 \rangle$ (orange) states. In the presence of quantum projection noise and classical readout noise, the outcomes follow broadened Poissonian (or Gaussian) distributions centered at $x_{\left | 0 \right \rangle}$ and $x_{\left | 1 \right \rangle}$. The finite overlap between the two distributions leads to misassignment errors, characterized by the probabilities $\kappa_0$ and $\kappa_1$. Crucially, physical asymmetries—such as $T_1$ relaxation in superconducting qubits or state-dependent decay in NV centers—result in an unequal overlap, where the "dark" error rate typically outweighs the "bright" error rate. This asymmetry induces a persistent measurement bias that imposes a systematic limit on sensing fidelity, which can be mitigated through the amplified response of non-Hermitian dynamics.
• Figure 3: Scaling behavior of correlated background detection noise. We consider power-law correlations in the background noise, with the correlation function defined as $C(|i-j|)\sim |i-j|^{-\gamma}$, where the exponent $\gamma$ governs the spatial decay rate. (a) Total noise correlation $\sum_{i,j}C_{ij}$ as a function of the number of measurements $N$ for different values of $\gamma$. In the short-range regime ($\gamma>1$), the total sum exhibits standard linear scaling $\sum_{i,j}C_{ij}\propto N$. In contrast, for long-range correlations ($\gamma<1$), the sum diverges super-extensively as $\sum_{i,j}C_{ij}\propto N^{\beta}$ with $\beta=2-\gamma$. (b) The extracted scaling exponent $\beta$ as a function of the correlation exponent $\gamma$. A clear crossover occurs at the critical value $\gamma=1$: for $\gamma>1$, the noise is effectively uncorrelated with $\beta\approx 1$, whereas for $\gamma<1$, the scaling is dominated by long-range dependencies, following the predicted relation $\beta=2-\gamma$. This superlinear growth of background noise directly impacts the metrological gain of non-Hermitian sensors in practical environments.
• Figure 4: Measurement precision under correlated background detection. We compare the estimation precision of the parameter $\lambda$ for Hermitian and non-Hermitian sensors in the presence of background noise with long-range correlations characterized by the exponent $\beta$. Parameters of the non-Hermitian sensing are set to $t = \pi/2\mathcal{E}$ with $a=1$, $\delta = 0.3$, $\mathcal{E}=0.5$, $\lambda=0.01$. (a) Precision as a function of the correlation coefficient $\beta$ for a fixed number of measurements $N=1000$. The non-Hermitian protocol demonstrates a significant enhancement over the Hermitian counterpart as $\beta$ approaches $2$, a regime where long-range correlations severely degrade standard sensing performance. (b) Scaling of the precision with the measurement repetitions $N$ for highly correlated noise ($\beta=1.8$), Notably, the non-Hermitian sensor displays an apparent advantage in measurement precision over the Hermitian counterpart.
• Figure 5: Schematic diagram of the photodetector.The horizontal and vertical polarization states($\left| H\right\rangle, \left| V\right\rangle$) of a photon are commonly used to encode two orthogonal quantum states, and their measurement can be realized using a polarization beam splitter(PBS). Detector 1 and detector 2 are photodetectors, which measure the two different polarization directions of photons obtained through the beam splitter. The number of photons measured by the two detectors follows a normal distribution.