  A quantum positioning system (QPS) is proposed that can provide a user with
all four of his space-time coordinates. The user must carry a corner cube
reflector, a good clock, and have a two-way classical channel of communication
with the origin of the reference frame. Four pairs of entangled photons
(biphotons) are sent through four interferometers: three interferometers are
used to determine the user's spatial position, and an additional interferometer
is used to synchronize the user's clock to coordinate time in the reference
frame. The spatial positioning part of the QPS is similar to a classical
time-of-arrival (TOA) system, however, a classical TOA system (such as GPS)
must have synchronized clocks that keep coordinate time and therefore the
clocks must have long-term stability, whereas in the QPS only a photon
coincidence counter is needed and the clocks need only have short-term
stability. Several scenarios are considered for a QPS: one is a terrestrial
system and another is a space-based-system composed of low-Earth orbit (LEO)
satellites. Calculations indicate that for a space-based system, neglecting
atmospheric effects, a position accuracy below the 1 cm-level is possible for
much of the region near the Earth. The QPS may be used as a primary system to
define a global 4-dimensional reference frame.
