Security and entanglement in differential-phase-shift quantum key distribution

TL;DR

This paper formalizes the differential-phase-shift quantum key distribution protocol as an entanglement-based scheme and demonstrates that its security relies on Bob's measurement detecting entanglement through non-commuting POVMs.

Contribution

It provides a formal equivalence between prepare-and-measure and entanglement-based protocols and establishes a necessary security condition involving Bob's measurement.

Findings

Bob's measurement detects entanglement via non-commuting POVMs

The protocol's security condition is satisfied

Formal equivalence between schemes is established

Abstract

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.