Eur. Phys. J. D 56, 441-444 (2010)
https://doi.org/10.1140/epjd/e2009-00303-6

Implementation of the Deutsch-Jozsa algorithm violates nonlocal realism

Obihiro University of Agriculture and Veterinary Medicine, Obihiro, Japan

Corresponding author: ko_mi_na1@yahoo.co.jp

Received: 11 May 2009
Revised: 7 October 2009
Published online: 8 December 2009

Abstract

The theoretical resource state for the implementation of the Deutsch-Jozsa algorithm is a multiqubit pure uncorrelated state. We show that N-qubit pure uncorrelated quantum states cannot admit rotationally invariant nonlocal realistic theories with a violation factor of 3^N. We find the violation factor 3^N when the measurement setup is entire range of settings for each of the observers, that is, considering rotationally invariant nonlocal realistic theories along with the property of a correlation function in the quantum theory. The implementation of the Deutsch-Jozsa algorithm theoretically relying on N-qubit pure uncorrelated states rules out rotationally invariant nonlocal realism with a violation factor of 3^N in an ideal case. Our analysis relies on the property of theoretical resource states for the algorithm. We cannot simulate the Deutsch-Jozsa algorithm by using rotationally invariant nonlocal realistic theories due to the property of theoretical resource states for the algorithm.