Bell's theorem and non-linear systems

LPMC, Ecole Normale Supérieure - 24 rue Lhomond, 75231 Paris cedex 5 and IEF Université Paris-Sud, Bât. 220 - 91405 Orsay cedex, France

Received: 9 July 1999
Accepted: 8 February 2000

Abstract

For all Einstein-Podolsky-Rosen–type experiments on deterministic systems the Bell inequality holds, unless non-local interactions exist between certain parts of the setup. Here we show that in non-linear systems the Bell inequality can be violated by non-local effects that are arbitrarily weak. Then we show that the quantum result of the existing Einstein-Podolsky-Rosen–type experiments can be reproduced within deterministic models that include arbitrarily weak non-local effects.