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As they can travel long distances, free space optical quantum states are goodcandidates for carrying information in quantum information technologyprotocols. These states, however, are often complex to produce and requireprotocols whose success probability drops quickly with an increase of the meanphoton number. Here we propose a new protocol for the generation and growth ofarbitrary states, based on one by one coherent adjunctions of the simple statesuperposition $\alpha | 0 > +\beta | 1 >$. Due to the nature of the protocol,that allows for the use of quantum memories, it can outperform existingprotocols.

Iterative tailoring of optical quantum states with homodyne measurements