**1.3.2 Advanced experiments**

By the 1970s, work piloted by [Clauser et al. (1969)], Aspect et al. (1982) was using an experimental approach to test Bell Inequalities and to clearly show a significant gap between Bell Inequalities and real quantum reality.

After 40 years of development, many accurate experiments [Lindner et al. (2005); Zeh (1970); Zeilinger et al. (2005)] have been performed successfully worldwide using Laser, NMRI, large molecular, quantum coding and quantum communication approaches [Afshar et al. (2007); Barrow et al. (2004); Fox (2006); Merali (2007); Schleich et al. (2007)]. Following the application of advanced technologies and simulation methodologies, detailed single and multiple photon detection technologies have been further developed.

### **1.3.3 Weakness**

However it does not matter how successful any single experiment or indeed many experiments might be, those results cannot simply replace the idea experiment of [Feynman et al. (1965,1989); Hawking & Mlodinow (2010); Penrose (2004)]. From a theoretical viewpoint, modern experiments involving Bell Inequations are excellent in illustrating the fundamental differences between a local realism and quantum reality. Since both theoretical and experimental activities focused on supporting or disproving Bell Inequalities cannot on their own provide a full explanation, further investigations are essential to provide a sound foundation on which a full understanding of quantum issues can be constructed.

#### **1.4 From local interactive measurements to global matrix representations**

In this chapter, a double path model has been established using the Mach-Zehnder interferometer. Different approaches to quantum measurements taken by Einstein, Stern-Gerlach, CHSH and Aspect are investigated to form quaternion structures. Using multiple-variable logic functions and variant principles, logic functions can be transferred into variant logic expressions as variant measures. Under such conditions, a variant simulation and representation model is proposed.

Fig. 1. (a-b) Double Path Model (a) Mach-Zehnder Double Path Model (b) Description Model

A given logic function *f* , can be represented as two meta logic functions *f*<sup>+</sup> and *f*<sup>−</sup> to simulate single and double path conditions. *N* bits of input vectors are exhausted by 2*<sup>N</sup>* states for measured data, recursive data are organized into eight histograms. Results are determined by symmetry/anti-symmetry properties in histograms. All 22*<sup>n</sup>* functions are applied to generate a set of histograms. Eight sets of histograms are represented as eight matrices in a selected C code configuration. Under this construction, it is possible to visualize different combinations from symmetry and anti-symmetry categories.

From these results, both additive probability properties in particle condition and wave interference properties with non-addition behaviors are observed. Both types of result are obtained consistently from this model under synchronous/asynchronous conditions. From a simulation viewpoint, this system satisfies all of Feynman's criteria conditions for double slit experiments.
