Preparing highly entangled quantum states between remote parties is a majorchallenge for quantum communications [1-8]. Particularly promising in thiscontext are the N00N states, which are entangled N-photon wavepacketsdelocalized between two different locations, providing measurement sensitivitylimited only by the uncertainty principle [1, 10-15]. However, these states arenotoriously vulnerable to losses, making it difficult both to share thembetween remote locations, and to recombine them to exploit interferenceeffects. Here we address this challenge by utilizing the reverse version of theHong-Ou-Mandel effect [16] to prepare a high-fidelity two-photon N00N stateshared between two parties connected by a lossy optical channel. Furthermore,we demonstrate that the enhanced phase sensitivity can be directly exploited inthe two distant locations, and we remotely prepare superpositions of coherentstates, known as Schr\"odinger's cat states" [17, 18].
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