We derive a formula for p(n) (the number of partitions n) in terms the partial Bell polynomials using Faà di Bruno’s and Euler’s pentagonal theorem.

Relatively few families of Bell inequalities have previously been identified. Some examples are the trivial, CHSH, Imm22, and CGLMP inequalities. This paper presents a large number of new families of tight Bell inequalities for the case of many observables. For example, 44,368,793 inequivalent tight Bell inequalities other than CHSH are obtained for the case of 2 parties each with 10 2-valued o...

Greenberger, Horne, Shimony and Zeilinger gave a new version of the Bell theorem without using inequalities (probabilities). Mermin summarized it concisely; but Bohm and Hiley criticized Mermin’s proof from contextualists’ point of view. Using the Branching Space-time language, in this paper a proof will be given that is free of these difficulties. At the same time we will also clarify the limi...

We introduce a two-observer all-versus-nothing proof of Bell's theorem which reduces the number of required quantum predictions from 9 to 4, provides a greater amount of evidence against local realism, reduces the detection efficiency requirements for a conclusive experimental test of Bell's theorem, and leads to a Bell inequality which resembles Mermin's inequality for three observers but requ...

Many claim that the security model developed by Bell and LaPadula and used as a basis for numerous prototype military computer systems is superior to others partly because its authors prove a "Basic Security Theorem" that applies to it. This paper shows that the theorem does not support such claims since it can be proven for security models that are obviously not secure. Further, the theorem pr...

Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisin's theorem). We show that there exist pure entangled N>2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko in...