Whether quantum mechanics can be almighty even in information science

TL;DR

The paper identifies a fundamental contradiction within quantum mechanics's formalism, questioning its axiomatic basis and implications for quantum information processing, including Deutsch's algorithm.

Contribution

It reveals a crucial contradiction in quantum formalism related to the existence of directions in spin-1/2 systems and measurement assumptions, challenging the foundations of quantum theory.

Findings

Contradiction between quantum predictions and the existence of directions in spin-1/2 systems

Implication that quantum formalism may lack a consistent axiomatic basis

Questioning of the validity of Deutsch's algorithm within current quantum theory

Abstract

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.