%0 Journal Article
%T Von Neumann¡¯s Theory, Projective Measurement, and Quantum Computation
%A Koji Nagata
%A Tadao Nakamura
%J Journal of Applied Mathematics and Physics
%P 874-897
%@ 2327-4379
%D 2015
%I Scientific Research Publishing
%R 10.4236/jamp.2015.37108
%X We discuss the fact that there is a crucial contradiction within Von Neumann¡¯s theory. We derive a proposition concerning a quantum expected value under an assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1 ¡Ü N < +¡Þ). This assumption intuitively depictures our physical world. However, the quantum predictions within the formalism of Von Neumann¡¯s projective measurement violate the proposition with a magnitude that grows exponentially with the number of particles. We have to give up either the existence of the directions or the formalism of Von Neumann¡¯s projective measurement. Therefore, Von Neumann¡¯s theory cannot depicture our physical world with a violation factor that grows exponentially with the number of particles. The theoretical formalism of the implementation of the Deutsch-Jozsa algorithm relies on Von Neumann¡¯s theory. We investigate whether Von Neumann¡¯s theory meets the Deutsch-Jozsa algorithm. We discuss the fact that the crucial contradiction makes the quantum-theoretical formulation of Deutsch-Jozsa algorithm questionable. Further, we discuss the fact that projective measurement theory does not meet an easy detector model for a single Pauli observable. Especially, we systematically describe our assertion based on more mathematical analysis using raw data. We propose a solution of the problem. Our solution is equivalent to changing Planck¡¯s constant
to a new constant
. It may be said that a new type of the quantum theory early approaches Newton¡¯s theory in the macroscopic scale than the old quantum theory does. We discuss how our solution is used in an implementation of Deutsch¡¯s algorithm.
%K Von Neumann¡¯s Theory
%K Projective Measurement
%K and Quantum Computation
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=58052