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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2401.16225 |
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| _version_ | 1866910727595360256 |
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| author | de Visme, Marc Vilmart, Renaud |
| author_facet | de Visme, Marc Vilmart, Renaud |
| contents | 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 qu$d$it 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16225 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimality in Finite-Dimensional ZW-Calculi de Visme, Marc Vilmart, Renaud Quantum Physics 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 qu$d$it 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. |
| title | Minimality in Finite-Dimensional ZW-Calculi |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.16225 |