One-dimensional Eigenvalue distributions of random sequences for FFT non-stationary randomness

摘要

In modern photon statistics, classical and quantum behavior can be distinguished by various quantum states of photon statistical distributions: Poisson (coherent/semi-classical wave behavior), and sub-Poisson (compressed state/particle behavior). Since this type of measurement mechanism is often associated with advanced laser/optical or photonic techniques, can this type of distribution model be modeled using discrete 0-1 sequences? In this paper, several sets of simulation modes are designed, and FFT transformation is used to extract relevant eigenvalues. Following the processing methods in the variant construction, special filters are constructed using the quantum random sequence provided by ANU (Australian national university), and conditional random sub-sequences are collected as input sequences. Multiple segments are separated from a random sequence, and relevant eigenvalues of FFT are selected to form a special set of eigenvalues. The shift operations are used to transform each sequence, showing obvious non-stationary random effects on various maps.