The Garden-Hose Game: A New Model of Computation, and Application to Position-Based Quantum Cryptography

We study position-based cryptography in the quantum setting. We examine a class of protocols that only require the communication of a single qubit and 2n bits of classical information. To this end, we define a new model of communication complexity, the gardenhose model, which enables us to prove upper bounds on the number of EPR pairs needed to attack such schemes. This model furthermore opens up a way to link the security of quantum position-based cryptography to traditional complexity theory.

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