Quantum Inf Process (2013) 12:3785–3789
An additional condition for Bell experiments
for accepting local realistic theories
Koji Nagata · Tadao Nakamura
Received: 20 July 2013 / Accepted: 23 August 2013 / Published online: 12 September 2013
© Springer Science+Business Media New York 2013
Abstract We assume that one source of two uncorrelated spin-carrying particles emits
them in a state, which can be described as a spin-1/2 bipartite pure uncorrelated state.
We consider a Bell–Clauser–Horne–Shimony–Holt (Bell–CHSH) experiment with
two-orthogonal-settings. We propose an additional condition for the state to be repro-
ducible by the property of local realistic theories. We use the proposed measurement
theory in order to construct the additional condition (Nagata and Nakamura in Int
J Theor Phys 49:162, 2010). The condition is that local measurement outcome is
2. Otherwise, such an experiment does not allow for the existence of local real-
istic theories even in the situation that all Bell–CHSH inequalities hold. Also we derive
new set of Bell inequalities when local measurement outcome is ±1/
Keywords Quantum measurement theory · Quantum non locality · Formalism
As a famous physical theory, the quantum theory (cf. [1–5]) gives accurate and at
times remarkably accurate numerical predictions. Much experimental data has ﬁt to
the quantum predictions for long time.
Fine shows [6,7] that quantum correlation functions accept local realistic theo-
ries if and only if all Bell–Clauser–Horne–Shimony–Holt (CHSH) inequalities hold.
However, is matrix theory compatible with probability theory? Matrix theory has pos-
tulates. Probability theory has postulates. We consider joint set of such postulates.
K. Nagata (
1-17-107 West 19 South 3, Obihiro, Hokkaido 080-2469, Japan
Department of Information and Computer Science, Keio University,
3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan