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We discuss several methods for unambiguous state discrimination of Nsymmetric coherent states using linear optics and photodetectors. One type ofmeasurements is shown to be optimal in the limit of small photon numbers forany N. For the special case of N=4 this measurement can be fruitfully used bythe receiving end (Bob) in an implementation of the BB84 quantum keydistribution protocol using faint laser pulses. In particular, if Bob detectsonly a single photon the procedure is equivalent to the standard measurementthat he would have to perform in a single-photon implementation of BB84, if hedetects two photons Bob will unambiguously know the bit sent to him in 50% ofthe cases without having to exchange basis information, and if three photonsare detected, Bob will know unambiguously which quantum state was sent.Comment: 5 RevTeX pages, 2 eps figure

Unambiguous state discrimination of coherent states with linear optics: Application to quantum cryptography