The ZX-calculus is incomplete for quantum mechanics

Published 14 Apr 2014 in cs.LO, math.CT, and quant-ph | (1404.3633v3)

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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