A quantum cloning game with applications to quantum position verification

TL;DR

This paper introduces a quantum cloning game involving multiple parties, analyzes its optimal success probability, and applies the findings to enhance security in quantum position verification protocols.

Contribution

It provides the first exact analysis of a quantum cloning game with multiple parties and demonstrates its implications for secure quantum position verification.

Findings

Optimal winning probability decays exponentially with repeated plays

Security of quantum routing protocol is established in the parallel setting

Results have applications in quantum cryptography, especially position verification

Abstract

We introduce a quantum cloning game in which $k$ separate collaborative parties receive a classical input, determining which of them has to share a maximally entangled state with an additional party (referee). We provide the optimal winning probability of such a game for every number of parties $k$, and show that it decays exponentially when the game is played $n$ times in parallel. These results have applications to quantum cryptography, in particular in the topic of quantum position verification, where we show security of the routing protocol (played in parallel), and a variant of it, in the random oracle model.