Maximal violation of Bell inequalities by position measurements

TL;DR

This paper demonstrates that maximal violations of the CHSH-Bell inequality can be achieved using only position measurements on entangled particles, with settings determined by measurement times, challenging certain hidden variable theories.

Contribution

It introduces a method to violate Bell inequalities through position measurements at different times, expanding the scope of quantum nonlocality tests.

Findings

Maximal Bell violations achieved with position measurements at different times.

Violations depend on how outcomes are assigned to positions.

Results challenge hidden variable theories like Bohm and Nelson.

Abstract

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.