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## Abstract

The category of Hilbert modules may be interpreted as a naive quantum field theory over a base space. Open subsets of the base space are recovered as idempotent subunits, which form a meet-semilattice in any firm braided monoidal category. There is an operation of restriction to an idempotent subunit: it is a graded monad on the category, and has the universal property of algebraic localisation. Spacetime structure on the base space induces a closure operator on the idempotent subunits. Restriction is then interpreted as spacetime propagation. This lets us study relativistic quantum information theory using methods entirely internal to monoidal categories. As a proof of concept, we show that quantum teleportation is only successfully supported on the intersection of Alice and Bob's causal future.

Original language | English |
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Title of host publication | The 14th International Conference on Quantum Physics and Logic (QPL) |

Publisher | Open Publishing Association |

Pages | 399–410 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 7 Jul 2017 |

Event | 14th International Conference on Quantum Physics and Logic - Nijmegen, Netherlands Duration: 3 Jul 2017 → 7 Jul 2017 http://qpl.science.ru.nl/ |

### Publication series

Name | Electronic Proceedings in Theoretical Computer Science |
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Publisher | Open Publishing Association |

Volume | 266 |

ISSN (Electronic) | 2075-2180 |

### Conference

Conference | 14th International Conference on Quantum Physics and Logic |
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Abbreviated title | QPL 2017 |

Country | Netherlands |

City | Nijmegen |

Period | 3/07/17 → 7/07/17 |

Internet address |

## Keywords

- math.CT
- quant-ph

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## Projects

- 1 Finished