Barros discusses that [Jose Acacio de Barros, Int. J. Theor. Phys. 50,
1828 (2011)] Nagata derives inconsistencies from quantum mechanics [K. Nagata,
Int. J. Theor. Phys. 48, 3532 (2009)]. Barros considers that the
inconsistencies do not come from quantum mechanics, but from extra assumptions
about the reality of observables. Here we discuss the fact that there is a
contradiction within the quantum theory. We discuss the fact that only one
expected value in a spin-1/2 pure state 〈σ_{x}〉rules out the reality of the
observable. We do not accept extra assumptions about the reality of
observables. We use the actually measured results of quantum measurements (raw
data). We use a single Pauli observable. We stress that we can use the quantum
theory even if we give up the axiomatic system for the quantum theory.

Acacio de Barros, J. (2011) Comments on “There Is No Axiomatic System for the Quantum Theory”. International Journal of Theoretical Physics, 50, 1828-1830. http://dx.doi.org/10.1007/s10773-011-0696-z

Nagata, K. (2009) There is No Axiomatic System for the Quantum Theory. International Journal of Theoretical Physics, 48, 3532-3536. http://dx.doi.org/10.1007/s10773-009-0158-z

Schon, C. and Beige, A. (2001) Analysis of a Two-Atom Double-Slit Experiment Based on Environment-Induced Measurements. Physical Review A, 64, Article ID: 023806. http://dx.doi.org/10.1103/PhysRevA.64.023806

Nagata, K. and Nakamura, T. (2010) Can von Neumann’s Theory Meet the Deutsch-Jozsa Algorithm? International Journal of Theoretical Physics, 49, 162-170. http://dx.doi.org/10.1007/s10773-009-0189-5

Nagata, K. and Nakamura, T. (2013) An Additional Condition for Bell Experiments for Accepting Local Realistic Theories. Quantum Information Processing, 12, 3785-3789. http://dx.doi.org/10.1007/s11128-013-0635-4