Impossibility of perfect cheating for single-qubit position verification

Abstract

In quantum position verification (QPV), a prover certifies her location to a set of verifiers by performing a quantum computation. One of the first QPV protocols was proposed by Kent, Munro, and Spiller in 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. Several variants of this protocol have been proposed and analyzed, but the question of whether the original protocol is secure has never been fully resolved. In this work we show that there is no perfect finite-dimensional cheating strategy for the single-qubit measurement protocol. Our proof uses tools from real algebraic geometry.

7 pages

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