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Pré-Publication, Document De Travail Année : 2024

Minimality in Finite-Dimensional ZW-Calculi

Minimality in Finite-Dimensional ZW-Calculi

Résumé

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 accommodate all finite dimensional Hilbert spaces at the same time. We again show the completeness of the provided equational theory.
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Dates et versions

hal-04496193 , version 1 (08-03-2024)

Identifiants

  • HAL Id : hal-04496193 , version 1

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Renaud Vilmart, Marc de Visme. Minimality in Finite-Dimensional ZW-Calculi. 2024. ⟨hal-04496193⟩
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