Multiphoton Knill-Laflamme-Milburn states generated by nonlinear optics

The Knill-Laflamme-Milburn (KLM) entangled state, proposed by Knill et al. in Nature409, 46 (2001)NATUAS0028-083610.1038/35051009, has unique advantages for linear optics quantum information processing tasks, because it is able to decrease the error rate. In this paper, we propose scalable schemes to generate the multi-qubit KLM entangled states with single-photon resources and weak cross-Kerr nonlinearity theoretically. We first construct the two-qubit KLM state, through which the three- and other n-qubit KLM states are generated. For the schemes using weak cross-Kerr nonlinearity, P homodyne measurement has a higher success rate than X homodyne measurement but with narrow applications since |αeiθ⟩ and |αe−iθ⟩ are distinguished from each other, which is undesirable for most of the entanglement generation schemes. To avoid this disadvantage, Jin et al. [Phys. Rev. A75, 054302 (2007)PLRAAN1050-294710.1103/PhysRevA.75.054302] introduced the coherent state superposition (CSS), c(|α⟩+|−α⟩), to generate a Greenberger-Horne-Zeilinger state but with a rapid oscillation term, which needs to be ignored. Through designing the optical path uniquely and choosing the phase of cross-Kerr nonlinearity suitably, our P homodyne measurement and CSS probe mode-based schemes to generate the KLM state avoid the needless term. The present scalable schemes have high total success probabilities, high fidelities even in consideration of decoherence, and may find potential applications in the future with the further development of nonlinear optics.