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Can Hidden Variables Theories Meet Quantum Computation?

Koji Nagata, Tadao Nakamura

Published Jan 1, 2015• 0 citations

Abstract

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.

DOI: 10.4236/oalib.1101804

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OALib

Can Hidden Variables Theories Meet Quantum Computation?

Koji Nagata, Tadao Nakamura

Published Jan 1, 2015• 0 citations

Publisher

Abstract

DOI: 10.4236/oalib.1101804

Related papers

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+1

-1

) does not meet a hidden variables model for a single Pauli observable. Hence we cannot introduce a classical probability space for the projective measurement theory in this case. Our discussion provides new insight to formulate quantum measurement theory, by using the measurement theory based on the truth values.

N

-item database using

O({N}^{1∕3})

queries, as opposed to

O({N}^{1∕2})

queries with Grover's search algorithm. On the other hand, the

{N}^{1∕3}

bound is optimal, meaning that we could probably not solve

\mathrm{NP}

-complete problems in polynomial time. We thus obtain the first good example of a model of computation that appears slightly more powerful than the quantum computing model.

N

spin-1/2 systems (

1 \leq N < +\infty

). 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 (

\hbar

) to a new constant (

\hbar/\sqrt{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.