The ZX calculus is incomplete for quantum mechanics

@inproceedings{Witt2014TheZC,
  title={The ZX calculus is incomplete for quantum mechanics},
  author={C. S. D. Witt and Vladimir Zamdzhiev},
  booktitle={QPL},
  year={2014}
}
We prove that the ZX-calculus is incomplete for quantum mechanics. We suggest the addition of a new 'color-swap' rule, of which currently no analytical formulation is known and which we suspect may be necessary, but not sufficient to make the ZX-calculus complete. 

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  • 2019
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