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Accurate knowledge of the spectral features of noise and their influence onopen quantum systems is fundamental for quantitative understanding andprediction of the dynamics in a realistic environment. For the weakmeasurements of two-level systems, the weak value obtained from experimentswill inevitably be affected by the noise of the environment. Following ourearlier work on the technique of the auto-correlative weak-value amplification(AWVA) approach under a Gaussian noise environment, here we study the effect ofnon-Gaussian noise on the AWVA technique.In particular, two types of noise witha negative-dB signal-to-noise ratio, frequency-stationary noises andfrequency-nonstationary noises are studied. The various frequency-stationarynoises, including low-frequency (1/f) noises, medium-frequency noises, andhigh-frequency noises, are generated in Simulink by translating the Gaussianwhite noise with different band-pass filters. While impulsive noise is studiedas an example of frequency-non stationary noises. Our simulated resultsdemonstrate that 1/f noises and impulsive noises have greater disturbance onthe AWVA measurements. In addition, adding one kind of frequency-stationarynoise, clamping the detected signals, and dominating the measurement range may{have} the potential to improve the precision of the AWVA technique with both asmaller deviation of the mean value and a smaller error bar in the presence ofmany hostile non-Gaussian noises.

The Effect of Non-Gaussian Noise on Auto-correlative Weak-value Amplification