The ZX-calculus is incomplete for quantum mechanics

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Abstract

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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De Witt, C. S., & Zamdzhiev, V. (2014). The ZX-calculus is incomplete for quantum mechanics. In Electronic Proceedings in Theoretical Computer Science, EPTCS (Vol. 172, pp. 285–292). Open Publishing Association. https://doi.org/10.4204/EPTCS.172.20

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