Tight relation between the physical effects of a quantum measurement and the information gained about an observable

Quantum Physics [Submitted on 4 Jun 2026] Tight relation between the physical effects of a quantum measurement and the information gained about an observable Natsuki Ogo, Holger F. Hofmann The dynamics of quantum measurements defines a precise relation between the information gained about one physical property of a system and the observable changes in another physical property of the same system. Here, we express this relation in terms of the Hilbert space superpositions of the corresponding eigenstates and show how the probability of an observable physical change can be obtained from the Bayesian update of the probabilities associated with the information obtained in the measurement. Our analysis demonstrates that the superposition principle provides the tightest possible expression of the trade-off between information and back action in a quantum measurement. Comments: 8 pages Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.05767 [quant-ph]   (or arXiv:2606.05767v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2606.05767 Focus to learn more Submission history From: Natsuki Ogo [view email] [v1] Thu, 4 Jun 2026 06:48:24 UTC (11 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-06 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)