Loss-tolerant position-based quantum cryptography

Position-based quantum cryptography (PBQC) allows a party to use its geographical location as its only credential to implement various cryptographic protocols. Such a protocol may lead to important applications in practice. Although it has been shown that any PBQC protocol is breakable if the adversaries pre-share an arbitrarily large entangled state, the security of PBQC in the bounded-quantum-storage model is still an open question. In this paper, we study the performance of various PBQC protocols over a lossy channel under the assumption that no entanglement is pre-shared between adversaries. By introducing the decoy state idea, we show that an extended Bennett-Brassard-1984-type PBQC protocol implemented with a weak coherent source and realistic single-photon detectors can tolerate an overall loss (including both the channel loss and the detection efficiency) of 13 dB if the intrinsic quantum bit error rate is 1%. We also study a few continuous variable PBQC protocols and show that they suffer from a 3-dB loss limitation.