Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions

@inproceedings{Booth2022CompleteZF,
  title={Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions},
  author={Robert Ivan Booth and Titouan Carette},
  booktitle={MFCS},
  year={2022}
}
We introduce a family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions. These calculi recover many of the nice features of the qubit ZX-calculus which were lost in previous proposals for higher-dimensional systems. We then prove that these calculi are complete, i.e. provide a set of rewrite rules which can be used to prove any equality of stabiliser quantum operations. Adding a discard construction, we obtain a calculus complete for mixed state… 

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