We propose and experimentally implement a novel reconfigurable quantum key distribution (QKD) scheme, where the users can switch in real time between conventional QKD and the recently-introduced measurement-device-independent (MDI) QKD. Through this setup, we demonstrate the distribution of quantum keys between three remote parties connected by only two quantum channels, a previously unattempted task. Moreover, as a prominent application, we extract the first quantum digital signature (QDS) rates from a network that uses a measurement-device-independent link. In so doing, we introduce an efficient protocol to distil multiple signatures from the same block of data, thus reducing the statistical fluctuations in the sample and increasing the final QDS rate.
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