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Journal of Modern Optics

Variant simulation system using quaternion structures

Jeffrey Zheng, Chris Zheng

Published Feb 2, 2012• 19 citations
Publisher

Abstract

Quantum measures play a key role in quantum interactions. In this paper, a variant simulation system – a variant double path model – is proposed that uses multiple variable logic functions and variant principle schemes applied to input/output relationships as a variant quaternion. Under this mechanism, a two-state system of quantum interactions can be simulated by the variant double path model. Visual distributions can be expressed by their probability, synchronous/asynchronous, and symmetry/anti-symmetry statistical properties. The simulation system can output eight histograms with different symmetric properties. Sample results are illustrated by two groups of 16 histograms for their intrinsic distributions. Critical evidence from Afshar's experiments is discussed. This particle model is fully capable of simulating double path experiments in systematic methodologies.

DOI
10.1080/09500340.2011.636152

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Quantum measures play a key role in quantum interactions. In this paper, a variant simulation system – a variant double path model – is proposed that uses multiple variable logic functions and variant principle schemes applied to input/output relationships as a variant quaternion. Under this mechanism, a two-state system of quantum interactions can be simulated by the variant double path model. Visual distributions can be expressed by their probability, synchronous/asynchronous, and symmetry/anti-symmetry statistical properties. The simulation system can output eight histograms with different symmetric properties. Sample results are illustrated by two groups of 16 histograms for their intrinsic distributions. Critical evidence from Afshar's experiments is discussed. This particle model is fully capable of simulating double path experiments in systematic methodologies.
Double slit experiments play a key role in Quantum Theory in distinct particle and wave interactions according to Feynman. In this paper, double path models together with variant logic principles are applied to establish a simulation system enabling the exhaustive testing of given targets. Using Einstein quanta interaction, different quaternion measures are investigated. Under conditions of Symmetry / Anti-symmetry and Synchronous / Asynchronous interaction, eight groups of statistical results are generated and presented as eight histograms showing the distributions. From this set of simulation results, it can be seen that not only is the synchronous condition the key factor in generating quantum wave interference patterns but also that the asynchronous condition is the key factor in classical particle distributions. Sample results are illustrated and explanations are discussed.
Using measure model and statistical approches to simulate quantum interaction on binary level systems,multiple interactive conditions are simulated via double path interference measures.From quantum interaction,Einstein,Mach-Zehnder,Stern-Gerlach and CHSH measuring parameters are investigated.Using multiple variable logic functions and variant principle,N bit vectors of 0-1 input/output pairs form variant quaternion to establish variant double path simulation model.Using probability,symmetry/anti-symmetry,sychronous/asychronous conditions,simulation system generates two groups of eight histograms to express their statistical distributions in relevant conditions.
Abstract Double-slit experiment plays a key role in Quantum Theory to distinct particle and wave interactions according to Feynman’s claims. In this chapter, double path model and variant logic principle are applied to establish a simulation system for exhaustive testing targets. Using Einstein quanta interaction, different measure quaternion structures are investigated. Under Symmetry/Anti-symmetry and Synchronous/Asynchronous interaction conditions, eight groups of statistical results are generated as eight histograms to show their distributions. From this set of simulation results, it can be recognized that the synchronous condition is the key fact to generate quantum wave interference patterns and, in addition, the asynchronous condition is the key fact to make classic particle distributions. Sample results are illustrated and explanations are discussed.
Two quantum interactive experiments are shown in strong wave-like interference properties,ie Young double slit experiment and very lower intensive and very long time explosin experiment for quanta.This paper is based on a classical statistic scheme: Bayes statistics on Conditional Probability to propose conditional probability measurements and relevant statistcal models to visualized complex properties of their interactions.Variant measurement simulation model is established and corresponding measring equations and perameters are formulated.Two typical cases are selected and each time has corresponding to four groups of results in 16 histograms.Under this construction,it is feasible to understand the intrinsic wave-like properties of quantum interactions.Under the conditional probability model,intrinsic wave-like statistical distributions are observed on both normal conditions and interferenced conditions in their spatial statistical distributions respectively.
Digital quantum simulation (DQS) has emerged as a powerful approach to investigate complex quantum systems using digital quantum computers. Such systems, like many-particle bosonic systems and intricate optical experimental setups, pose significant challenges for classical simulation methods. In this paper, we utilize a general formalism for the DQS of bosonic systems, which consists of mapping bosonic operators to Pauli operators using the Gray code, in order to simulate interferometric variants of Afshar’s experiment—an intricate optical experiment—on IBM’s quantum computers. We investigated experiments analogous to Afshar’s double-slit experiment performed by Unruh and Pessoa Júnior, exploring discussions on the apparent violation of Bohr’s complementarity principle when considering the entire experimental setup. Based on the aforementioned experiments, we construct a variation of a delayed-choice setup. We also explore another experiment starting with a two-photon initial state. Finally, we analyze these experiments within the framework of an updated quantum complementarity principle, which applies to specific quantum state preparations and remains consistent with the foundational principles of Quantum Mechanics.