Phase randomization improves the security of quantum key distribution

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.