Intrinsic Geometry of Operational Contexts: A Riemannian-Style Framework for Quantum Channels
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917146657816576 |
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| author | Yoshida, Kazuyuki |
| author_facet | Yoshida, Kazuyuki |
| contents | We propose an intrinsic geometric framework on the space of operational contexts, specified by channels, stationary states, and self-preservation functionals. Each context C carries a pointer algebra, internal charges, and a self-consistent configuration minimizing a self-preservation functional. The Hessian of this functional yields an intrinsic metric on charge space, while non-commutative questioning loops dN -> dPhi -> d rho^circ define a notion of curvature. In suitable regimes, this N-Q-S geometry reduces to familiar Fisher-type information metrics and admits charts that resemble Riemannian or Lorentzian space-times. We outline how gauge symmetries and gravitational dynamics can be interpreted as holonomies and consistency conditions in this context geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intrinsic Geometry of Operational Contexts: A Riemannian-Style Framework for Quantum Channels Yoshida, Kazuyuki Quantum Physics Mathematical Physics 81P45, 83C45, 46L53, 62B10 We propose an intrinsic geometric framework on the space of operational contexts, specified by channels, stationary states, and self-preservation functionals. Each context C carries a pointer algebra, internal charges, and a self-consistent configuration minimizing a self-preservation functional. The Hessian of this functional yields an intrinsic metric on charge space, while non-commutative questioning loops dN -> dPhi -> d rho^circ define a notion of curvature. In suitable regimes, this N-Q-S geometry reduces to familiar Fisher-type information metrics and admits charts that resemble Riemannian or Lorentzian space-times. We outline how gauge symmetries and gravitational dynamics can be interpreted as holonomies and consistency conditions in this context geometry. |
| title | Intrinsic Geometry of Operational Contexts: A Riemannian-Style Framework for Quantum Channels |
| topic | Quantum Physics Mathematical Physics 81P45, 83C45, 46L53, 62B10 |
| url | https://arxiv.org/abs/2512.12944 |