**8. Main results**

Presented as predictions and conjectures:

#### **8.1 Predictions**

Commensurate with the chapter of local interactive measurements, similar predictions can be described under conditional probability conditions:

**Prediction 1:** Left distributions have relationships showing polarized vertical behaviors with intrinsic wave properties on conditional environments.

**Prediction 2:** Right distributions have relationships showing polarized horizontal behaviors with intrinsic wave properties on conditional environments.

**Prediction 3:** D-P distributions have relationships showing classical particle statistical behaviors with intrinsic wave properties on conditional environments.

**Prediction 4:** D-W distributions have relationships showing wave interference statistical behaviors with strong wave properties on conditional environments.

**Prediction 5:** Afshar's experiments are a special case of the EPR model in real photon experimental environments.

**Prediction 6:** Distributions on conditional environments provide essential evidence to support a series of experimental results on quanta self-interference properties.

#### **8.2 Conjectures**

Presented in relation to milestones in the historical debate underpinning the foundations of QM:

**Conjecture 1.** Einstein may be declared the winner in the Bohr-Einstein debates on QM.

**Conjecture 2.** EPR construction is a super-powerful model to support different measurements and simulations of quantum behaviors.

**Conjecture 3.** The variant construction provides a logical measurement based foundation to support the simulation and visualization of quantum behaviors.

**Conjecture 4.** The next generation of fundamental development in QM will grow out of further theoretical and experimental exploration based on variant construction.

#### **9. Conclusion**

Long held views on the wave/particle enigma, especially those investigated through single photon experiments may be founded on a special case rather than a general explanation. Further insight may be found working from conditional probability measurements to global matrix representation on the variant construction.

Applying conditional probability models on interactive measurements and relevant statistical processes, two groups of parameters {*u*˜*β*, *v*˜*β*} describe left path, right path, D-P and D-W conditions with distinguishing symmetry and anti-symmetry properties. {*PH*(*u*˜*β*|*J*), *PH*(*v*˜*β*|*J*)} provide eight groups of distributions under symmetry and anti-symmetry forms. In addition, {*M*(*u*˜*β*), *M*(*v*˜*β*)} provide eight matrices to illustrate global behaviors under conditional environments.

The complexity of *n*-variable function space has a size of 22*<sup>n</sup>* and exhaustive vector space has 2*N*. Overall simulation complexity is determined by *O*(22*<sup>n</sup>* <sup>×</sup> <sup>2</sup>*N*) as ultra exponent productions. How to overcome the limitations imposed by such complexity and how best to compare and contrast such simulations with real world experimentation will be key issues in future work.

Six predictions and four conjectures are offered for testing by further theoretical and experimental work.

#### **10. Acknowledgements**

Thanks to Colin W. Campbell for help with the English edition, to The School of Software Engineering, Yunnan University and The Key Laboratory of Yunnan Software Engineering for financial supports to the Information Security research projects (2010EI02, 2010KS06) and sub-CDIO project.
