TITLE:
Can Von Neumann’s Theory Meet Quantum Computation?
AUTHORS:
Koji Nagata, Tadao Nakamura
KEYWORDS:
Quantum Measurement Theory, Quantum Computer, Formalism
JOURNAL NAME:
Open Access Library Journal,
Vol.2 No.8,
August
24,
2015
ABSTRACT: Recently, 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 the directions 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 the directions. Therefore, we have to give up either the existence
of the directions or the formalism of von Neumann’s projective measurement.
Hence, there is a crucial contradiction within von Neumann’s theory. We discuss
that this crucial contradiction makes the theoretical formulation of Deutsch’s
algorithm questionable. Especially, we systematically describe our assertion
based on more mathematical analysis using raw data. Our discussion, here,
improves previously published argumentations very much.