The differential-phase-shift quantum key distribution protocol is formalised as a prepare-and-measure scheme and translated into an equivalent entanglement-based protocol. A necessary condition for security is that Bob's measurement can detect the entanglement of the distributed state in the entanglement-based translation, which implies that his measurement is described by non-commuting POVM elements. This condition is shown to be met.
@article{arxiv.1002.0953,
title = {Security and entanglement in differential-phase-shift quantum key distribution},
author = {Adriana Marais and Thomas Konrad and Francesco Petruccione},
journal= {arXiv preprint arXiv:1002.0953},
year = {2010}
}