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Abstract

The design of quantum protocols for secure key generation poses many
challenges: On the one hand, they need to be practical concerning experimental
realisations. On the other hand, their theoretical description must be simple
enough to allow for a security proof against all possible attacks. Often, these
two requirements are in conflict with each other, and the differential phase
shift (DPS) QKD protocol is an excellent example of this: It is designed to be
implementable with current optical telecommunication technology, which, for
this protocol, comes at the cost that many standard security proof techniques
do not apply to it. In this work, we give the first full security proof of DPS
QKD against general attacks, including finite-size effects. The proof combines
techniques from quantum information theory, quantum optics, and relativity. We
first give a security proof of a QKD protocol whose security stems from
relativistic constraints. We then show that DPS QKD can be formulated as an
instance of the relativistic protocol. In addition, we show that coherent
attacks on the DPS protocol are, in fact, stronger than collective attacks.