TY - JOUR

T1 - Maximal violation of Bell inequalities by position measurements

AU - Kiukas, Jukka

AU - Werner, Reinhard F.

N1 - Funding information: This work was supported by Finnish Cultural Foundation, Academy of Finland, and the EU Integrated Project SCALA.

PY - 2010

Y1 - 2010

N2 - We show that it is possible to find maximal violations of the CHSH-Bell inequality using only position measurements on a pair of entangled non-relativistic free particles. The device settings required in the CHSH inequality are done by choosing one of two times at which position is measured. For different assignments of the "+" outcome to positions, namely to an interval, to a half line, or to a periodic set, we determine violations of the inequalities, and states where they are attained. These results have consequences for the hidden variable theories of Bohm and Nelson, in which the two-time correlations between distant particle trajectories have a joint distribution, and hence cannot violate any Bell inequality.

AB - We show that it is possible to find maximal violations of the CHSH-Bell inequality using only position measurements on a pair of entangled non-relativistic free particles. The device settings required in the CHSH inequality are done by choosing one of two times at which position is measured. For different assignments of the "+" outcome to positions, namely to an interval, to a half line, or to a periodic set, we determine violations of the inequalities, and states where they are attained. These results have consequences for the hidden variable theories of Bohm and Nelson, in which the two-time correlations between distant particle trajectories have a joint distribution, and hence cannot violate any Bell inequality.

U2 - 10.1063/1.3447736

DO - 10.1063/1.3447736

M3 - Article

VL - 51

SP - 072105

JO - J. Math. Phys.

JF - J. Math. Phys.

SN - 1089-7658

IS - 7

ER -