Continuous-variable quantum position verification secure against entangled attackers

A continuous-variable (CV) quantum position verification (QPV) protocol was recently studied and proven to be secure if and only if attackers do not preshare any entanglement. In the discrete-variable (DV) analog of that protocol, it had been shown that modifying how the classical challenge is sent from the verifiers to the prover leads to a lower bound on the amount of entanglement needed by the attackers. In this work we show that similar conclusions can be drawn for CV QPV. We design a CV QPV protocol in which the quantum part of the challenge is a coherent state and the classical part consists of 𝑛-bit strings coming from both verifiers. We show that the protocol is secure against attackers who have fewer than 𝑐⁢𝑛 preshared entangled qubits, where 𝑐 is a constant. The security proof is given for a certain range of attenuation and excess noise and holds even if the quantum information travels arbitrarily slowly.