Andrea Olivo

Position verification is a cryptographic primitive aiming at securely certifying the location of a party in space. Informationally-secure PV was shown to be impossible through the existence of universal attacks both in the classical setting [Chandran et al., 2009] and in the quantum setting [Buhrman et al., 2014; Beigi and König,2011]. However, while classical attacks require the same amount of resources than the protocol, known universal quantum attacks make use of an exponential amount of entanglement through a technique known as Instantaneous Nonlocal Quantum Computation. In this paper, we characterize attacks to a "BB84-like" protocol already proposed in previous work [Kent et al., 2011], based on single photons polarized at an angle θ. We consider adversaries sharing maximally entangled pairs of qudits and find low-dimensional INQC attacks. We find exact attacks against some rational angles, including some sitting outside of the Clifford hierarchy (e.g. π/6), and show no θ allows to tolerate errors higher than ~0.5% against adversaries holding two ebits per protocol's qubit.