Position-based cryptography: Single-qubit protocol secure against multi-qubit attacks

While it is known that unconditionally secure position-based cryptography is impossible both in the classical and the quantum setting, it has been shown that some quantum protocols for position verification are secure against attackers which share a quantum state of bounded dimension. In this work, we consider the security of the qubit routing protocol. The protocol has the advantage that an honest prover only has to manipulate a single qubit and a classical string of length $2n$. We show that the protocol is secure if each of the attackers holds at most $n/2 - 3$ qubits. With this, we show for the first time that there exists a quantum position verification protocol where the ratio between the quantum resources an honest prover needs and the quantum resources the attackers need to break the protocol is unbounded. The verifiers need only increase the amount of classical resources to force the attackers to use more quantum resources. Finally, we show that the qubit routing protocol is robust with respect to noise, making it appealing for applications.