Complete ZX-calculi for the stabiliser fragment in odd prime dimensions

Autor:	Booth, Robert I., Carette, Titouan
Rok vydání:	2022
Předmět:	Quantum Physics
Zdroj:	MFCS 2022, 24:1-24:15
Druh dokumentu:	Working Paper
DOI:	10.4230/LIPIcs.MFCS.2022.24
Popis:	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 stabiliser quantum mechanics in odd prime dimensions, and this furthermore gives a complete axiomatisation for the related diagrammatic language for affine co-isotropic relations. Comment: 23 pages + 31 pages of references and appendices; more corrections
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.12531 Zobrazit plný text záznamu View this record from Arxiv