Practical quantum key distribution with geometrically uniform states

In this paper we propose a practical quantum key distribution protocol based on geometrically uniform states and a standard decoy state technique. The protocol extends the ideas used in SARG04 to the limit where the core quantum communication is secure against unambiguous state discrimination and provides some level of inherent resistance to photon number splitting attacks. An additional decoy state overlay ensures its conformity to the conventional security requirements. The protocol security is analyzed by an explicit construction of the most optimal unitary attack, which is known to reach the tight security bound in the case of BB84.