  Ideal quantum key distribution (QKD) protocols call for a source that emits
single photon signals, but the sources used in typical practical realizations
emit weak coherent states instead. A weak coherent state may contain more than
one photon, which poses a potential security risk. QKD with weak coherent state
signals has nevertheless been proven to be secure, but only under the
assumption that the phase of each signal is random (and completely unknown to
the adversary). Since this assumption need not be fully justified in practice,
it is important to know whether phase randomization is really a requirement for
security rather than a convenient technical assumption that makes the security
proof easier. Here, we exhibit an explicit attack in which the eavesdropper
exploits knowledge of the phase of the signals, and show that this attack
allows the eavesdropper to learn every key bit in a parameter regime where a
protocol using phase-randomized signals is provably secure. Thus we demonstrate
that phase randomization really does enhance the security of QKD using weak
coherent states. This result highlights the importance of a careful
characterization of the source for proofs of the security of quantum key
distribution.
