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.
%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
}