Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum complementarity and logical indeterminacy   Whenever a mathematical proposition to be proved requires more information
than it is contained in an axiomatic system, it can neither be proved nor
disproved, i.e. it is undecidable, or logically undetermined, within this
axiomatic system. I will show that certain mathematical propositions on a
d-valent function of a binary argument can be encoded in d-dimensional quantum
states of mutually unbiased basis (MUB) sets, and truth values of the
propositions can be tested in MUB measurements. I will then show that a
proposition is undecidable within the system of axioms encoded in the state, if
and only if the measurement associated with the proposition gives completely
random outcomes.

20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org