2026-07-23T21:29:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:22806 2025-02-03T10:18:32Z ddc:004 open_access

Minimality in Finite-Dimensional ZW-Calculi de Visme, Marc Vilmart, Renaud Quantum Computing Categorical Quantum Mechanics ZW-calculus Qudits Finite Dimensional Hilbert Spaces Completeness Minimality The ZW-calculus is a graphical language capable of representing 2-dimensional quantum systems (qubit) through its diagrams, and manipulating them through its equational theory. We extend the formalism to accommodate finite dimensional Hilbert spaces beyond qubit systems. First we define a qudit version of the language, where all systems have the same arbitrary finite dimension d, and show that the provided equational theory is both complete - i.e. semantical equivalence is entirely captured by the equations - and minimal - i.e. none of the equations are consequences of the others. We then extend the graphical language further to allow for mixed-dimensional systems. We again show the completeness and minimality of the provided equational theory. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marc de Visme and Renaud Vilmart 2025 Is Part Of LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2025.49 urn:nbn:de:0030-drops-228067 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.49 eng https://creativecommons.org/licenses/by/4.0/legalcode