  Exchanging light pulses to perform accurate space-time positioning is a
paradigmatic issue of physics. It is ultimately limited by the quantum nature
of light, which introduces fluctuations in the optical measurements and leads
to the so-called Standard Quantum Limit (SQL). We propose a new scheme
combining homodyne detection and mode-locked femtosecond lasers that lead to a
new SQL in time transfer, potentially reaching the yoctosecond range
(10^-21-10^-24 s). We prove that no other measurement strategy can lead to
better sensitivity with shot noise limited light. We then demonstrate that this
already very low SQL can be overcome using appropriately multimode squeezed
light. Benefitting from the large number of photons used in the experiment and
from the optimal choice of both the detection strategy and of the quantum
resource, the proposed scheme represents a significant potential improvement in
space-time positioning.
