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Open Quantum Systems Decoherence

A compositional approach to quantum functions

arXiv
Authors: Benjamin Musto, David Reutter, Dominic Verdon

Year

2017

Paper ID

24973

Status

Preprint

Abstract Read

~2 min

Abstract Words

106

Citations

N/A

Abstract

We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum graphs, which captures the quantum graphs and quantum graph homomorphisms recently discovered in the study of nonlocal games and zero-error communication, and relates them to quantum automorphism groups of graphs considered in the setting of compact quantum groups. We show that the 2-categories of quantum sets and quantum graphs are semisimple and characterise existing notions of quantum permutations and quantum graph isomorphisms as dagger-dualisable 1-morphisms in these 2-categories.

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  • This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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  • We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1711.07945 [2] arXiv https://arxiv.org/abs/1711.07945 [3] Publisher https://arxiv.org/abs/1711.07945

Local Citation Graph (Related-Paper Links)

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