Dispersion cancellation and nonclassical noise reduction for large-photon-number states

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/√N reduction in noise below the classical shot noise limit in precise timing applications, as was previously suggested by Giovannetti, Lloyd, and Maccone [Nature (London) 412, 417 (2001)]. 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, anticorrelated states, and frequency-entangled coherent states, which shows that these effects are a fundamental result of entanglement.