Breaking simple quantum position verification protocols with little entanglement

TL;DR

This paper demonstrates that simple quantum position verification protocols can be compromised using low-entanglement attacks, revealing vulnerabilities even with minimal entanglement resources.

Contribution

It introduces exact low-dimensional INQC attacks against practical QPV protocols based on single-photon polarization, expanding understanding of protocol vulnerabilities.

Findings

Exact attacks for rational angles including outside Clifford hierarchy

Error tolerance limited to approximately 0.005 with two ebits per qubit

Vulnerabilities exist even with minimal entanglement resources

Abstract

Instantaneous nonlocal quantum computation (INQC) evades apparent quantum and relativistic constraints and allows to attack generic quantum position verification (QPV) protocols (aiming at securely certifying the location of a distant prover) at an exponential entanglement cost. We consider adversaries sharing maximally entangled pairs of qudits and find low-dimensional INQC attacks against the simple practical family of QPV protocols based on single photons polarized at an angle $\theta$. We find exact attacks against some rational angles, including some sitting outside of the Clifford hierarchy (e.g. $\pi/6$), and show no $\theta$ allows to tolerate errors higher than $\simeq 5\cdot 10^{-3}$ against adversaries holding two ebits per protocol's qubit.