  Quantum enhancement of optical pulse timing accuracy is investigated in the
Heisenberg picture. Effects of optical loss, group-velocity dispersion, and
Kerr nonlinearity on the position and momentum of an optical pulse are studied
via Heisenberg equations of motion. Using the developed formalism, the impact
of decoherence by optical loss on the use of adiabatic soliton control for
beating the timing standard quantum limit [Tsang, Phys. Rev. Lett. 97, 023902
(2006)] is analyzed theoretically and numerically. The analysis shows that an
appreciable enhancement can be achieved using current technology, despite an
increase in timing jitter mainly due to the Gordon-Haus effect. The decoherence
effect of optical loss on the transmission of quantum-enhanced timing
information is also studied, in order to identify situations in which the
enhancement is able to survive.
