Purification and detection of entangled coherent states

In [J. C. Howell and J. A. Yeazell, Phys. Rev. A 62, 012102 (2000)], a proposal is made to generate entangled macroscopically distinguishable states of two spatially separated traveling optical modes. We model the decoherence due to light scattering during the propagation along an optical transmission line and propose a setup allowing an entanglement purification from a number of preparations which are partially decohered due to transmission. A purification is achieved even without any manual intervention. We consider a nondemolition configuration to measure the purity of the state as contrast of interference fringes in a double-slit setup. Regarding the entangled coherent states as a state of a bipartite quantum system, a close relationship between purity and entanglement of formation can be obtained. In this way, the contrast of interference fringes provides a direct means to measure entanglement.