dorsal/arxiv
View SchemaRepresentation theorem for obsevables on a quantum logic
| Authors | Andrei Khrenikov, Olga Nánásiová |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0302053 |
| URL | https://arxiv.org/abs/quant-ph/0302053 |
Abstract
We study a conditional state on a quantum logic using Renyi's approach (or Bayesian principle). This approach helps us to define independence of events and differently from the situation in the classical theory of probability, if an event $a$ is independent of an event $b$, then the event $b$ can be dependent on the event $a$. We will show that we can define a $s$-map (function for simultaneous measurements on a quantum logic). It can be shown that if we have the conditional state we can define the $s$-map and conversely. By using the $s$-map we can introduce joint distribution also for noncompatible observables on a quantum logic.
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"date_created": "2026-03-02T18:01:56.401000Z",
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"abstract": "We study a conditional state on a quantum logic using Renyi\u0027s approach (or\nBayesian principle). This approach helps us to define independence of events\nand differently from the situation in the classical theory of probability, if\nan event $a$ is independent of an event $b$, then the event $b$ can be\ndependent on the event $a$. We will show that we can define a $s$-map (function\nfor simultaneous measurements on a quantum logic). It can be shown that if we\nhave the conditional state we can define the $s$-map and conversely. By using\nthe $s$-map we can introduce joint distribution also for noncompatible\nobservables on a quantum logic.",
"arxiv_id": "quant-ph/0302053",
"authors": [
"Andrei Khrenikov",
"Olga N\u00e1n\u00e1siov\u00e1"
],
"categories": [
"quant-ph"
],
"title": "Representation theorem for obsevables on a quantum logic",
"url": "https://arxiv.org/abs/quant-ph/0302053"
},
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"execution_id": "7b5a49fa-bdfa-4f5c-96d2-6d7e11728e50",
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"variant": "snapshot-2026-03-01",
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