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Protocols for quantum position verification (QPV) which combine classical andquantum information are insecure in the presence of loss. We study the exactloss-tolerance of the most popular protocol for QPV, which is based on BB84states, and generalizations of this protocol. By bounding the winningprobabilities of a variant of the monogamy-of-entanglement game usingsemidefinite programming (SDP), we find tight bounds for the relation betweenloss and error for these extended non-local games.  These new bounds enable the usage of QPV protocols using more-realisticexperimental parameters. We show how these results transfer to the variantprotocol which combines $n$ bits of classical information with a single qubit,thereby exhibiting a protocol secure against a linear amount of entanglement(in the classical information $n$) even in the presence of a moderate amount ofphoton loss. Moreover, this protocol stays secure even if the photon encodingthe qubit travels arbitrarily slow in an optical fiber. We also extend thisanalysis to the case of more than two bases, showing even strongerloss-tolerance for that case.  Finally, since our semi-definite program bounds a monogamy-of-entanglementgame, we describe how they can also be applied to improve the analysis ofone-sided device-independent QKD protocols.

Single-qubit loss-tolerant quantum position verification protocol secure against entangled attackers