Bottom line - the price of locality is slavery, no free will. Free will is maximized in the nonlocal universe seems to be the conclusion of this paper.

Jonathan Barrett

H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, U.K.

Nicolas Gisin

Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland

(Dated: August 24, 2010)

*If nonlocality is to be inferred from a violation of Bell’s inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the hypothetical local variables. We study the case where this assumption is weakened, so that measurement settings and local variables can be at least partially correlated. We demonstrate a connection between this type of model and classical communication models, and a connection with models that exploit the detection efficiency loophole. We show that even if Bob enjoys full free will, if Alice lacks a single bit of free will - in the sense that the mutual information between local variables and her measurement setting is one bit - then all correlations obtained from projective measurements on a singlet can be reproduced by local means.*

*Quantum nonlocality, whereby particles appear to in- fluence one another instantaneously even though they are widely separated in space, is one of the most remarkable phenomena known to modern science [1–3]. Historically, this peculiar prediction of quantum theory triggered many debates and even doubts about its validity [4]. Today, it is a well established experimental fact [5], although the profound implications for our world view remain controversial. In order to demonstrate quantum nonlocality, measurements are performed on separated entangled quantum systems, and it is shown that the measurement outcomes are correlated in a manner that cannot be accounted for by local variables. In order to conclude that nonlocality is exhibited, it is crucial for the analysis that the choices of which measurement to perform are freely made by the experimenters. Indeed, it is well known that if the measurement settings are not freely chosen, but depend on the hypothetical local variables, then all correlations can be reproduced. Here we reverse the argument. We take for granted that quantum correlations can be produced and ask, how much free will must the experimenters be assumed to have in order to rule out an explanation in terms of local variables [6]? We prove that if an experimenter Alice misses one single bit of free will - that is if the mutual information between her choice and the local variables is one bit - then correlations between two qubits in a singlet state can be reproduced by local variables, and no demonstration of nonlocality is possible. ...*

*This is a truly remarkable result. It means that if Al- ice is lacking “a single bit of free will”, then all correlations from projective measurements on a singlet state can be explained with local variables. If Alice delegates the choices of her inputs to a random number generator, this implies that if the random number generator has only a slight correlation to the hypothetical local variable λ, then a demonstration of nonlocality using a singlet state is impossible. ...*

*Let us emphasize the change in paradigm since the old EPR paper [4]. If, contrary to EPR, one accepts non- locality as a fact, then not only can one develop pow- erful applications in quantum information science, like device-independent quantum key distribution [12] and random number generators [21], but moreover one can upper bound the lack of free will of the players ! Conversely, if one player lacks a single bit of free will, then no demonstration of nonlocality with projective measurements on the singlet state is possible.*