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PreprintCC BY 4.0HAL

Picturing general quantum subsystems

  • Octave Mestoudjian
  • Matt Wilson
  • Augustin Vanrietvelde
  • Pablo Arrighi
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Abstract

We extend the usual process-theoretic view on locality and causality in subsystems (based on the tensor product case) to general quantum systems (i.e. possibly non-factor, finite-dimensional von Neumann algebras). To do so, we introduce a primitive notion of splitting maps within dagger symmetric monoidal categories. Splitting maps give rise to subsystems that admit comparison via a preorder called comprehension, and support an adaptation of the usual categorical trace. We show that the comprehension preorder precisely captures the inclusion partial order between von Neumann algebras, and that the splitting map trace captures the natural notion of von Neumann algebra trace. As a consequence of the development of these diagrammatic tools, we prove that the known equivalence between semi-causality and semi-localisability for factor subsystems extends to all (including non-factor) subsystems.

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Cite

BibTeXRIS
BibTeX
@misc{mestoudjian2026picturing,
  title = {{Picturing general quantum subsystems}},
  author = {Octave Mestoudjian and Matt Wilson and Augustin Vanrietvelde and Pablo Arrighi},
  howpublished = {HAL},
  year = {2026},
  month = jul,
  eprint = {2511.09494},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05795121v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Picturing general quantum subsystems
AU  - Octave Mestoudjian
AU  - Matt Wilson
AU  - Augustin Vanrietvelde
AU  - Pablo Arrighi
PY  - 2026
DA  - 2026/07/03
PB  - HAL
UR  - https://hal.science/hal-05795121v1
AB  - We extend the usual process-theoretic view on locality and causality in subsystems (based on the tensor product case) to general quantum systems (i.e. possibly non-factor, finite-dimensional von Neumann algebras). To do so, we introduce a primitive notion of splitting maps within dagger symmetric monoidal categories. Splitting maps give rise to subsystems that admit comparison via a preorder called comprehension, and support an adaptation of the usual categorical trace. We show that the comprehension preorder precisely captures the inclusion partial order between von Neumann algebras, and that the splitting map trace captures the natural notion of von Neumann algebra trace. As a consequence of the development of these diagrammatic tools, we prove that the known equivalence between semi-causality and semi-localisability for factor subsystems extends to all (including non-factor) subsystems.
ER  -