%0 Generic %1 citeulike:478875 %A Fuchs, Christopher A. %D 2001 %K information quantum %T Quantum Foundations in the Light of Quantum Information %U http://arxiv.org/abs/quant-ph/0106166 %X 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, <a href="/abs/quant-ph/9909073">quant-ph/9909073</a>). 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.

@misc{citeulike:478875, 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, <a href="/abs/quant-ph/9909073">quant-ph/9909073</a>). 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.}, added-at = {2007-08-18T13:22:24.000+0200}, author = {Fuchs, Christopher A.}, biburl = {https://www.bibsonomy.org/bibtex/21e246a06c07a6846ed488f61cbcf60b1/a_olympia}, citeulike-article-id = {478875}, description = {citeulike}, eprint = {quant-ph/0106166}, interhash = {06cf9e88525ecaa475cfaedfa4b37a0e}, intrahash = {1e246a06c07a6846ed488f61cbcf60b1}, keywords = {information quantum}, month = Jun, priority = {2}, timestamp = {2007-08-18T13:22:36.000+0200}, title = {Quantum Foundations in the Light of Quantum Information}, url = {http://arxiv.org/abs/quant-ph/0106166}, year = 2001 }