Coherent eavesdropping strategies for the four state quantum cryptography protocol

An elementary derivation of best eavesdropping strategies for the 4 state BB84 quantum cryptography protocol is presented, for both incoherent and two--qubit coherent attacks. While coherent attacks do not help Eve to obtain more information, they are more powerful to reveal the whole message sent by Alice. Our results are based on symmetric eavesdropping strategies, which we show to be sufficient to analyze these kind of problems.