Figure 1 | Scientific Reports

Figure 1

From: Long-distance device-independent quantum key distribution

Figure 1

Schematic of the considered DIQKD protocol. While Alice holds an entanglement source, \({\rho }_{ab}\), in her lab, Bob holds a qubit amplifier, which consists of an entanglement source, \({\rho }_{bc}\), and a Bell state measurement (BSM) used for teleportation. The role of the qubit amplifier is to mitigate the effect of channel loss. In every round of the protocol in which a successful heralding takes place at the qubit amplifier, Bob randomly chooses a bit value \({T}_{i}\in \{0,1\}\). If \({T}_{i}=0\), Alice (Bob) chooses as measurement setting \({X}_{i}={\sigma }_{{\rm{z}}}\) (\({Y}_{i}={\sigma }_{{\rm{z}}}\)). If \({T}_{i}=1\), Alice chooses at random her measurement setting \({X}_{i}\in \{{\sigma }_{{\rm{z}}},{\sigma }_{{\rm{x}}}\}\), with \({\sigma }_{{\rm{z}}}\) and \({\sigma }_{{\rm{x}}}\) being the Pauli matrices given by Eq. (1). Similarly, in this latter case, Bob chooses at random his measurement setting \({Y}_{i}\in \left\{{\sigma }_{+},{\sigma }_{-}\right\}\), where \({\sigma }_{\pm }=({\sigma }_{{\rm{z}}}\pm {\sigma }_{{\rm{x}}})/\sqrt{2}\). Their respective outcomes are recorded as \({A}_{i},{B}_{i}\in \left\{0,1\right\}\), where \({A}_{i}\) (\({B}_{i}\)) indicates which of Alice’s (Bob’s) two photodetectors registered a single-photon pulse. If, say, Alice obtains an inconclusive result (i.e., no photons or multiple photons are observed, she deterministically selects \({A}_{i}=1\), and similarly for Bob. The reader is referred to the main text for further details.

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