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arXiv · 1504.07171

A Tight Lower Bound for the BB84-states Quantum-Position-Verification Protocol

Jérémy Ribeiro·Frédéric Grosshans
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Abstract

We use the entanglement sampling techniques developed by Dupuis, Fawzi and Wehner to find a lower bound on the entanglement needed by a coalition of cheater attacking the quantum position verification protocol using the four BB84 states in the scenario where the cheaters have no access to a quantum channel but share a (possibly mixed) entangled state $\tilde{\Phi}$. For a protocol using n qubits, a necessary condition for cheating is that the max- relative entropy of entanglement $E_{\max}(\tilde{\Phi})\ge n-O(\log n)$. This improves previously known best lower bound by a factor $\sim4$, and it is essentially tight, since this protocol is vulnerable to a teleportation based attack using $n-O(1)$ ebits of entanglement.

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Jérémy Ribeiro, Frédéric Grosshans. 2015-04-27. A Tight Lower Bound for the BB84-states Quantum-Position-Verification Protocol. https://arxiv.org/abs/1504.07171

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