On a recipe for quantum graphical languages

• URL: http://arxiv.org/abs/2008.04193v1
• Date: Mon, 10 Aug 2020 15:26:08 GMT
• Title: On a recipe for quantum graphical languages
• Authors: Titouan Carette and Emmanuel Jeandel
• Abstract summary: We classify Z*-algebras up to isomorphism in two dimensional Hilbert spaces and show that they are all variations of the aforementioned calculi. We do the same for linear relations and show that the calculus of [2] is essentially the unique one.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can wonder if new Z*-calculi will continue to be proposed forever. This article answers negatively. All those language share a common core structure we call Z*-algebras. We classify Z*-algebras up to isomorphism in two dimensional Hilbert spaces and show that they are all variations of the aforementioned calculi. We do the same for linear relations and show that the calculus of [2] is essentially the unique one.

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