%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