Title | Parallel Self-Testing of the GHZ State with a Proof by Diagrams |

Publication Type | Journal Article |

Year of Publication | 2019 |

Authors | Breiner, S, Kalev, A, Miller, C |

Journal | EPTCS |

Volume | 287 |

Pages | 43-66 |

Date Published | 01/29/2019 |

Abstract | Quantum self-testing addresses the following question: is it possible to verify the existence of a multipartite state even when one's measurement devices are completely untrusted? This problem has seen abundant activity in the last few years, particularly with the advent of parallel self-testing (i.e., testing several copies of a state at once), which has applications not only to quantum cryptography but also quantum computing. In this work we give the first error-tolerant parallel self-test in a three-party (rather than two-party) scenario, by showing that an arbitrary number of copies of the GHZ state can be self-tested. In order to handle the additional complexity of a three-party setting, we use a diagrammatic proof based on categorical quantum mechanics, rather than a typical symbolic proof. The diagrammatic approach allows for manipulations of the complicated tensor networks that arise in the proof, and gives a demonstration of the importance of picture-languages in quantum information. |

URL | https://arxiv.org/abs/1806.04744 |

DOI | 10.4204/EPTCS.287.3 |