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Infrared Remote Sensing and Instrumentation

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

Xin Zhang, Jeffrey Zheng

Published Sep 9, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2532035

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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.
From a quantum statistical viewpoint, four typical quantum states are Fock, Sub-Poissonian, Poissonian and SuperPoissonian states. Quantum interactions are focus among Fock and Poissonian states. Using quantum statistics, model and simulation, this paper proposes two models: matrix and variant transformations: 1. MT Matrix Transformation – eigenvalue states; 2. VT Variant Transformation – invariant states to analyze three random sequences: 1) random; 2) conditional random in a constant; 3) periodic pattern. Four procedures are proposed. Fast Fourier Transformation FFT is applied as one of MT schemes and two invariant scheme of VT schemes are applied, three random sequences are in M segments and each segment has a length m to generate a measuring sequence. Shifting operations are applied on each random sequence to create m+1 spectrum distributions. For FFT, a pair of eigenvalues are selected as the output. Two types of 1D and 2D variant maps are generated to illustrate multiple parameter selections to generate a series of results. Since sequences 1) and 3) are related simple, more cases are focus on sequences 2). Better than FFT, VT distinguishes various Fock, Sub-Poissonian, Poissonian states in random analysis to distinguish three random sequences as three levels of statistical ensembles: Micro-canonical, Canonical, and Grand-Canonical ensembles. Applying two transformations, quantum statistics, model and simulation of modern quantum theory and applications can be explored.
From a quantum statistical viewpoint, four typical quantum states are Fock, Sub-Poissonian, Poissonian and Super-Poissonian states. Quantum interactions are among Fock and Poissonian states. Using quantum statistics, model and simulation, this paper propose two models: matrix and variant transformations: 1. MT Matrix Transformation – eigenvalue states; 2. VT Variant Transformation – invariant states to analyze three random sequences: 1) random; 2) conditional random in a constant; 3) periodic pattern. Four procedures are proposed. Fast Fourier Transformation FFT is applied as one of MT schemes and two invariant scheme of VT schemes are applied, three random sequences are used in M segments, and each segment has a length m to generate a measuring sequence. Shifting operations are applied on each random sequence to create m+1 spectrum distributions. Better than FFT, VT can identify Fock, Sub-Poissonian, Poissonian states in random analysis to distinguish three random sequences as three levels of statistical ensembles: Micro-canonical, Canonical, and Grand-Canonical ensembles. Applying two transformations, quantum statistics, model and simulation of modern quantum theory and applications can be explored. Copyright © VBRI Press.
Abstract In this chapter, a testing model is used to apply statistical probability in multiple distributions on three maps for a selected sequence to check refined stationary randomness on quantum sequences. Three random data sequences are collected from two quantum random resources: one from Australian National University (ANU) and two (initial and secure) from University of Science and Technology of China (USTC). Multiple results are created on three maps, and measurements of stationary randomness are illustrated and compared. Three samples show distinct stationary properties.
Random numbers sequences (RNSs) play a vital role in various scientific and engineering applications. They are critical to the integrity of classical and quantum cryptography, the accuracy of mathematical modeling and Monte Carlo simulations, and the core mechanics of applications in fields as diverse as gambling and statistical sampling. While the primary criteria for RNSs sources are their quality and generation rate, their integration into experimental designs is equally significant for many fundamental physical tests and applications. This work presents a comparative analysis of optical random number generation architectures, which can be seamlessly included into various advanced classical and quantum optical experimental schemes. In particular, we evaluate the trade-off between the high generation rate of an attenuated laser (a quasi-single-photon source) and the superior statistical quality of a heralded single-photon source operating at a much lower frequency. To overcome the limitations of each individual source, we propose and examine a novel hybrid architecture that utilizes their mixed radiation, enabling the generation of highquality RNSs at an enhanced rate. Furthermore, we demonstrate that the raw sequences generated by such a source can not only exhibit but, in some cases, even surpass the degree of randomness achieved by sequences processed through powerful randomness extractors.
The statistical distribution for the number of bosons in a specified subsystem of a finite-dimensional multilevel system is obtained and investigated under conditions for which the total number of particles is a random variable characterized by the Poisson distribution. The resulting hyper-Poisson distribution is determined by the confluent hypergeometric function and contains as its particular limiting cases the Poisson distribution, as well as the single-mode and multimode thermal distributions. The developed model can be efficiently used to describe the thermal characteristics of bounded quantum systems, as well as in the problems of statistical reconstruction of optical quantum states, processes, and detectors.