Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Foundations in the Light of Quantum Information   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.

8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas