One of the important concepts in logical studies is the self-reference, which often leads to semantic inconsistencies. It is reviewed that the cyclical time process, particularly in terms of computing machines, may be useful in analyzing the peculiar aspects of self-reference. On the other hand, due to Bell’s inequalities, quantum entanglement is often considered a natural phenomenon that is distinguishable from classical theory. Moreover, entanglement has been shown to be an essential part of recent developments in quantum computing and quantum cryptography. In this paper, the entanglement swapping protocol is applied to four 2-level non-maximal states, and a new non-trivial class of nonmaximal states that approximate the weakest link is examined numerically. The initial part of the article will review some foundational and philosophical issues of quantum theory in regard to consciousness, while the latter will use numerical methods to discuss a practical aspect of quantum information science.

Numerical simulation, Entanglement, Network