  Nonlocal dispersion cancellation is generalized to frequency-entangled states
with large photon number N. We show that the same entangled states can
simultaneously exhibit a factor of 1/sqrt(N) reduction in noise below the
classical shot noise limit in precise timing applications, as was previously
suggested by Giovannetti, Lloyd and Maccone (Nature v412 (2001) p417). The
quantum-mechanical noise reduction can be destroyed by a relatively small
amount of uncompensated dispersion and entangled states of this kind have
larger timing uncertainties than the corresponding classical states in that
case. Similar results were obtained for correlated states, anti-correlated
states, and frequency-entangled coherent states, which shows that these effects
are a fundamental result of entanglement.
