  In quantum position verification, a prover certifies her location by
performing a quantum computation and returning the results (at the speed of
light) to a set of trusted verifiers. One of the very first protocols for
quantum position verification was proposed in (Kent, Munro, Spiller 2011): the
prover receives a qubit $Q$ from one direction, receives an orthogonal basis
$\{ v, v^\perp \}$ from the opposite direction, then measures $Q$ in $\{ v,
v^\perp \}$ and broadcasts the result. A number of variants of this protocol
have been proposed and analyzed, but the question of whether the original
protocol itself is secure has never been fully resolved. In this work we show
that there is no perfect finite-dimensional cheating strategy for the original
KMS measurement protocol. Our approach makes use of tools from real algebraic
geometry.
