The superposition theorem

P.V. Landshoff, Allen Metherell, Gareth Rees

S. Balasubramanian

A generalization to the Hellmann–Feynman theorem is presented when the quantum mechanical state is a linear superposition of energy eigenstates. Some simple applications are discussed.

Giacomo Mauro D’Ariano, Giulio Chiribella, Paolo Perinotti

Yingrui Yang

Being either true or false, 1 or 0, the standard logic and the Boolean algebra traditionality never rotate. Thus, it can only account for polarization states but not superposition states. This paper proves the Boolean rotation theorem through complexifications. This result allows us to formulate polarization spinors as well as superpositions spinors. It provides a new understanding of the Riemann sphere of two-state systems. It also provides an alternative solution to the measurement of wavefunctions, which accounts for both the U-process and the R-process. The work reported in this paper formulates the Penrose twistor geometry of the polarization spinors and the superposition spinors.

Leon Gunther

Ghenadie N. Mardari

Euclidean theorems are indisputable in flat spaces, but do not hold in curved spaces. Likewise, Bell’s Theorem is true for jointly distributed variables in Kolmogorov probability spaces. Yet, quantum spin variables are not jointly distributed and cannot coexist in Kolmogorov spaces. They have different qualities and operate by different rules. Therefore, Bell’s Theorem does not entail that quantum theory is non-local. The question remains: what is the origin of quantum contextuality? Other theories (not quantum theory) need nonlocality or super-determinism to make similar predictions, because they cannot violate Bell-type inequalities, but why is quantum theory different? The answer is found in the analysis of quantum superposition, in the context of a much older debate about the ontology of linear wave superposition.