Exceptional Points as Witnesses of Non-Gaussian Noise

Abstract

Efficient control of quantum devices requires the knowledge of their environmental noise, yet the commonly measured power spectrum does not fully characterize non-Gaussian fluctuations of realistic environments. Here we show that exceptional points (EPs) in the noise-averaged dephasing response can expose observable signatures of non-Gaussian statistics, distinguishing environments with identical lower-order statistics. We also introduce a theoretical model that describes dephasing environments in terms of identical independent noise sources while preserving the power spectrum. Given a calibrated single-source model, the largest EP order extracted from the measured dephasing response determines the number of sources and predicts the higher-order statistics of the combined noise. We illustrate an atomtronic readout that maps distinct EP signatures onto an evolving ensemble-averaged atomic interference pattern. Our results connect non-Hermitian dynamics to environmental noise statistics, providing a route to characterize noise in quantum devices used in computing, metrology, and precision measurement.

The paper asks whether exceptional points (EPs) in noise-averaged quantum coherence can distinguish classical dephasing environments with identical low-order statistics. It models stationary finite-state Markov noise through the tilted generator $G(\chi)=W-i\chi X$, with coherence $\Phi(\chi,t)=\mathbf{1}^T e^{G(\chi)t}\boldsymbol\pi$. An EP is considered observable when its Jordan-block polynomial survives this preparation and readout. An exactly solved three-state switching family has common covariance $C_2(\tau)=\sigma^2e^{-\gamma|\tau|}$ and vanishing odd multitime correlations. Two members therefore agree through third order but differ in fourth-order correlations. Their coherence responses exhibit, respectively, an EP$_3$ at $|\chi|=\gamma/(\sqrt{2}\sigma)$ and an EP$_2$ at $|\chi|\simeq0.52826\gamma/\sigma$. The former produces $e^{-\gamma t}(1+\gamma t/2)^2$; the latter contains a linear polynomial multiplying an exponential. These results follow from explicit projected-resolvent poles. Adding a common independent asymmetric background preserves the distinction while introducing nonzero third-order correlations. For a normalized sum of $M$ identical independent sources, tensor-product factorization establishes unchanged power spectrum, connected-correlation scaling $C_n^{(M)}=M^{1-n/2}C_n^{(1)}$, EP coupling proportional to $\sqrt M$, and visible order $R_M=1+M(r-1)$ for single-source order $r$. Thus source-number inference requires a calibrated single-source model and identical independent constituents; unequal rates or amplitudes generally separate their EP thresholds. The Gaussian limit moves these EPs to infinite coupling. An ideal rotationally invariant atomtronic ring maps coherence onto an ensemble-averaged density harmonic, including with rotationally invariant interactions. This is a theoretical readout illustration, not an experimental demonstration.