Lossy purification and detection of entangled coherent states

In work by Howell and Yeazell [Phys. Rev. A 62, 012102 (2000)], a proposal is made to generate entangled macroscopically distinguishable states of two spatially separated traveling optical modes. After considering a preparation with nonperfect photodetection, we discuss a random mode of entanglement purification without manual intervention using a number of preparations transmitted over a lossy optical transmission line. An efficiency greater than 1/2 of the purification scheme is required to increase entanglement at all. Furthermore, we study a nondemolition configuration to measure the purity of the state as contrast of interference fringes in a double-slit setup. As a consequence of the relationship between purity and entanglement of formation resulting from treating the entangled coherent states as a state of a bipartite quantum system, the contrast of interference fringes provides a direct means to measure entanglement.