We show that entanglement harvested from a quantum field
by interaction with local detectors undergoing anti-parallel acceleration can
be used to measure the distance of closest approach between the two detectors.
Information about the separation is stored nonlocally in the phase of the joint
state of the detectors after the interaction; a single detector alone contains
none. We model the detectors as two-level quantum systems accelerating
uniformly through the Minkowski vacuum
while interacting for a short time with a massless scalar field. This
interaction allows entanglement to be swapped locally from the field to the
detectors. Although each detector alone sees the same thermal spectrum (due to
Unruh radiation), the joint state between them may be entangled. In the
vicinity of a critical distance of closest approach between the detectors, the
phase of the entangled state depends sensitively on the distance. We contrast
this with the case of parallel acceleration, in which no such critical distance
exists, and we discuss the connection of this case with entanglement harvested
from an expanding universe.