Security and entanglement in differential-phase-shift quantum key distribution.
Quantum key distribution (QKD) aims at the creation of a secret key in the two locations of partners, traditionally Alice and Bob, wishing to communicate in private. A generic QKD protocol utilises a quantum channel and an authenticated classical channel for exchanges between partners in Phases 1 and 2 of the protocol, respectively. Phase 1 can be described as a prepareand- measure (P&M) or equivalently as an entanglement-based (EB) phase. Bob performs the same measurement in both descriptions. Subsequent to measurement, Phase 2 is commenced, the aim of which is to distill a secret key from the measurement outcomes resulting from Phase 1. A necessary condition for the security of a QKD protocol is that the measurement performed by Bob in Phase 1 must be described by non-commuting POVM elements. One method of proving the unconditional security of a QKD protocol is to show that the complete protocol (including Phases 1 and 2) is equivalent to an entanglement distillation protocol. A rst step towards showing such an equivalence for a given P&M QKD protocol is to describe an EB translation of Phase 1, where the condition on Bob's measurement is met. Di erential-phase-shift (DPS) QKD is a member of the class of distributedphase- reference QKD protocols. Unconditional security proofs for this class of protocols do not yet exist. Phase 1 of DPSQKD is here described and formalised as both a P&M and an EB phase, and Bob's measurement is shown to be described by non-commuting POVM elements. This description of an equivalent EB translation of DPSQKD where the condition on Bob's measurement is met, is a fi rst step towards a potential unconditional security proof for the protocol based on entanglement distillation.