Paper
Von Neumann’s Theory Does Not Meet Deutsch’s Algorithm
- Authors:
- Koji Nagata; Tadao Nakamura
- Abstract
- It is shown that there is a crucial contradiction within von Neumann’s theory [K. Nagata and T. Nakamura, Int. J. Theor. Phys. 49, 162 (2010)]. We derive a proposition concerning a quantum expected value under the assumption of the existence of z-axis and x-axis in a spin-1/2 system. The quantum predictions within the formalism of von Neumann’s projective measurement cannot coexist with the proposition concerning the existence of z-axis and x-axis. Therefore, we have to give up either the existence of z-axis and x-axis or the formalism of von Neumann’s projective measurement. Hence there is a crucial contradiction within von Neumann’s theory. Here we discuss the crucial contradiction of von Neumann’s theory by using a single Pauli observable. Further we discuss our argumentations by using actually happened results. Clearly, we do not assume reality of the observable. We discuss that this crucial contradiction makes the theoretical formulation of Deutsch’s algorithm questionable.
- Keywords
- Quantum Measurement Theory; Quantum Computer; Formalism
- StartPage
- 104
- EndPage
- 109
- Doi