Quantum Conditional Stochastic Processes

--> Quantum Physics arXiv:2603.27369 (quant-ph) [Submitted on 28 Mar 2026] Title: Quantum Conditional Stochastic Processes Authors: Stan Gudder View a PDF of the paper titled Quantum Conditional Stochastic Processes, by Stan Gudder View PDF HTML (experimental) Abstract: Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave functions, Born's rule for probabilities and others. If we accept that quantum mechanics is probabilistic, then these concepts can be derived and they become secondary. In this work, we begin with what we call a \textit{conditional stochastic process} (CSP) which is based on real numbers and probabilities. As we shall see, such processes are defined by three simple axioms. We then use CSP to derive quantum mechanics by employing a correspondence called a \textit{dictionary}. We also show that the converse holds. That is, beginning with a quantum system, we employ the dictionary to derive a CSP. Comments: 6 pages Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.27369 [quant-ph] (or arXiv:2603.27369v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.27369 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Stanley P. Gudder [ view email ] [v1] Sat, 28 Mar 2026 18:31:09 UTC (6 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Conditional Stochastic Processes, by Stan Gudder View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) Links to Code Toggle Papers with Code ( What is Papers with Code? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? )