dorsal/arxiv
View SchemaQuantum Foundations in the Light of Quantum Information
| Authors | Christopher A. Fuchs |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106166 |
| URL | https://arxiv.org/abs/quant-ph/0106166 |
Abstract
This paper reports three almost trivial theorems that nevertheless appear to have significant import for quantum foundations studies. 1) A Gleason-like derivation of the quantum probability law, but based on the positive operator-valued measures as the basic notion of measurement (see also Busch, quant-ph/9909073). Of note, this theorem also works for 2-dimensional vector spaces and for vector spaces over the rational numbers, where the standard Gleason theorem fails. 2) A way of rewriting the quantum collapse rule so that it looks almost precisely identical to Bayes rule for updating probabilities in classical probability theory. And 3) a derivation of the tensor-product rule for combining quantum systems (and with it the very notion of quantum entanglement) from Gleason-like considerations for local measurements on bipartite systems along with classical communication.
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"abstract": "This paper reports three almost trivial theorems that nevertheless appear to\nhave significant import for quantum foundations studies. 1) A Gleason-like\nderivation of the quantum probability law, but based on the positive\noperator-valued measures as the basic notion of measurement (see also Busch,\nquant-ph/9909073). Of note, this theorem also works for 2-dimensional vector\nspaces and for vector spaces over the rational numbers, where the standard\nGleason theorem fails. 2) A way of rewriting the quantum collapse rule so that\nit looks almost precisely identical to Bayes rule for updating probabilities in\nclassical probability theory. And 3) a derivation of the tensor-product rule\nfor combining quantum systems (and with it the very notion of quantum\nentanglement) from Gleason-like considerations for local measurements on\nbipartite systems along with classical communication.",
"arxiv_id": "quant-ph/0106166",
"authors": [
"Christopher A. Fuchs"
],
"categories": [
"quant-ph"
],
"title": "Quantum Foundations in the Light of Quantum Information",
"url": "https://arxiv.org/abs/quant-ph/0106166"
},
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