  In this paper, we propose quantum position-verification schemes where all the
channels are untrusted except the position of the prover and distant reference
stations of verifiers. We review and analyze the existing QPV schemes
containing some pre-shared data between the prover and verifiers. Most of these
schemes are based on non-cryptographic assumptions, that is, quantum/classical
channels between the verifiers are secure. It seems impractical in the
environment fully controlled by adversaries and would lead to security
compromise in practical implementations. However, our proposed formulism for
quantum position-verification is more robust, secure and according to the
standard assumptions of cryptography. Furthermore, once the position of the
prover is verified, our schemes establish secret keys in parallel and can be
used for authentication and secret communication between the prover and
verifiers.
