We study the relation between hidden variables theories and quantum computation.We discuss an inconsistency between a hidden variables theory and controllability of quantum computation.To derive the inconsistency, we use the maximum value of the square of an expected value.We propose a solution of the problem by using new hidden variables theory.Also we discuss an inconsistency between hidden variables theories and the double-slit experiment as the most basic experiment in quantum mechanics.This experiment can be an easy detector to Pauli observable.We cannot accept hidden variables theories to simulate the double-slit experiment in a specific case.Hidden variables theories may not depicture quantum detector.This is a quantum measurement theoretical profound problem.We study the relation between hidden variables theories and quantum computation.We discuss an inconsistency between a hidden variables theory and controllability of quantum computation.To derive the inconsistency, we use the maximum value of the square of an expected value.We propose a solution of the problem by using new hidden variables theory.Also we discuss an inconsistency between hidden variables theories and the double-slit experiment as the most basic experiment in quantum mechanics.This experiment can be an easy detector to Pauli observable.We cannot accept hidden variables theories to simulate the double-slit experiment in a specific case.Hidden variables theories may not depicture quantum detector.This is a quantum measurement theoretical profound problem.

OALibJan 1, 20150 citations

Stern-Gerlach Experiment, Quantum Phase Factor, and Hidden-Variables Theories

Koji Nagata, Tadao Nakamura

We discuss whether the Stern-Gerlach experiment accepts hidden-variables theories. We discuss that the existence of two spin-1/2 pure states $|\uparrow\rangle$ and $|\downarrow\rangle$ rules out the existence of probability space of specific quantum measurement. If we detect $|\uparrow\rangle$ , then measurement outcome is $+1$ . If we detect $|\downarrow\rangle$ , then measurement outcome is $-1$ . This hidden-variables theory does not accept the transition probability $|\langle\uparrow|\downarrow\rangle|^2=0$ . Therefore we have to give up the hidden-variables theory. This implies the Stern-Gerlach experiment cannot accept the specific hidden-variables theory. And we study whether quantum phase factor accepts hidden-variables theories. We use the transition probability for two spin-1/2 pure states $(|\uparrow\rangle+|\downarrow\rangle)/\sqrt{2}$ and $(|\uparrow\rangle+e^{i \theta}|\downarrow\rangle)/\sqrt{2}$ . It is $\cos^2(\theta/2)$ . We discuss that the phase factor does not accept another specific hidden-variables theory. We explore the phase factor is indeed a quantum effect, not classical. Our research gives a new insight to the quantum information processing which relies on quantum phase factor, such as Deutsch's algorithm.We discuss whether the Stern-Gerlach experiment accepts hidden-variables theories. We discuss that the existence of two spin-1/2 pure states $|\uparrow\rangle$ and $|\downarrow\rangle$ rules out the existence of probability space of specific quantum measurement. If we detect $|\uparrow\rangle$, then measurement outcome is $+1$. If we detect $|\downarrow\rangle$, then measurement outcome is $-1$. This hidden-variables theory does not accept the transition probability $|\langle\uparrow|\downarrow\rangle|^2=0$. Therefore we have to give up the hidden-variables theory. This implies the Stern-Gerlach experiment cannot accept the specific hidden-variables theory. And we study whether quantum phase factor accepts hidden-variables theories. We use the transition probability for two spin-1/2 pure states $(|\uparrow\rangle+|\downarrow\rangle)/\sqrt{2}$ and $(|\uparrow\rangle+e^{i \theta}|\downarrow\rangle)/\sqrt{2}$. It is $\cos^2(\theta/2)$. We discuss that the phase factor does not accept another specific hidden-variables theory. We explore the phase factor is indeed a quantum effect, not classical. Our research gives a new insight to the quantum information processing which relies on quantum phase factor, such as Deutsch's algorithm.

Mar 1, 20140 citations

A Hidden Variable Theory

The MIT Press eBooksMay 28, 20190 citations

The Status of Hidden-Variable Theories

Abner Shimony

Studies in logic and the foundations of mathematicsJan 1, 19736 citations

We discuss whether the Stern-Gerlach experiment accepts hidden-variables theories. We discuss that the existence of two spin-1/2 pure states

|\uparrow\rangle

and

|\downarrow\rangle

rules out the existence of probability space of specific quantum measurement. If we detect

|\uparrow\rangle

, then measurement outcome is

+1

. If we detect

|\downarrow\rangle

, then measurement outcome is

-1

. This hidden-variables theory does not accept the transition probability

|\langle\uparrow|\downarrow\rangle|^2=0

. Therefore we have to give up the hidden-variables theory. This implies the Stern-Gerlach experiment cannot accept the specific hidden-variables theory. And we study whether quantum phase factor accepts hidden-variables theories. We use the transition probability for two spin-1/2 pure states

(|\uparrow\rangle+|\downarrow\rangle)/\sqrt{2}

and

(|\uparrow\rangle+e^{i \theta}|\downarrow\rangle)/\sqrt{2}

. It is

\cos^2(\theta/2)

. We discuss that the phase factor does not accept another specific hidden-variables theory. We explore the phase factor is indeed a quantum effect, not classical. Our research gives a new insight to the quantum information processing which relies on quantum phase factor, such as Deutsch's algorithm.