Phase estimation, photon cloning and the Bernoulli map

A scheme for repeated cloning of photons through laser-atom interactions is considered and shown to be the optical analog of a network for relative-phase estimation. In both cases, the dynamics of an appropriate phase is governed by the Bernoulli shift map, resulting in information loss. The analysis is generalized to include a wide class of coherent states. © 2002 Elsevier Science B.V. All rights reserved.