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Can Von Neumann’s Theory Meet Quantum Computation?

Koji Nagata, Tadao Nakamura

Published Jan 1, 2015• 0 citations
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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.

DOI
10.4236/oalib.1101805

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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.
We discuss that there is a crucial contradiction within quantum mechanics. We derive a proposition concerning a quantum expecta-tion 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 the Hilbert space formalism of the quantum theory. This implies that there is no axiomatic system for the quantum theory. This also reveals that we need new physical theories in order to explain the handing of raw experimental data. We discuss that this crucial contradiction makes the quantum-theoretical formulation of Deutsch’s algorithm questionable. PACS: 03.67.Lx, 03.65.Ta, 03.65.Ca 1
We discuss that there is a crucial contradiction within quantum mechanics. We derive a proposition concerning a quantum expectation 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 the Hilbert space formalism of the quantum theory. This implies that there is no axiomatic system for the quantum theory. This also reveals that we need new physical theories in order to explain the handing of raw experimental data. We discuss that this crucial contradiction makes the quantum-theoretical formulation of Deutsch's algorithm questionable.
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 NNN spin-1/2 systems (1≤N<+∞1 \leq N < +\infty1≤N<+∞). 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 (ℏ\hbarℏ) to a new constant (ℏ/2\hbar/\sqrt{2}ℏ/2​). 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.
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 ≤ N 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.
Recently, [{arXiv:0810.3134}] is accepted and published. We present ultimate version of no-hidden-variables theorem. We derive a proposition concerning the quantum theory under the existence of the Bloch sphere in a single spin-1/2 system. The existence of a single classical probability space for measurement outcome within the formalism of von Neumann's projective measurement does not coexist with the proposition concerning the quantum theory. We have to give up the existence of such a classical probability space for measurement outcome in the two-dimensional Hilbert space formalism of the quantum theory. The quantum theory does not accept a hidden-variable interpretation in the two-dimensional space.