Quantum cloning bound and application to quantum key distribution

摘要

We introduce a quantum cloning bound which we apply to a straightforward and relatively direct security proofnof the prepare-and-measure Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol againstncollective attacks. The approach we propose is able to handle the practical problem of source and detectornalignment imprecisions in a simple way. Specifically, we derive a key-rate bound for a BB84 implementation innwhich Alice’s source emits four given but arbitrary pure states, where the usual equivalence between prepare-andmeasurenand entanglement-based QKD no longer applies. Our result is similar to a key rate derived by Marøynet al. [Phys. Rev. A 82, 032337 (2010)] and generally an improvement over the key rate derivable from thenentropic uncertainty relation in situations where it applies.We also provide a stronger result for a source emittingnarbitrary qubit states, and a further improved result if the detector is additionally assumed two dimensional.