Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computable functions, quantum measurements, and quantum dynamics   We construct quantum mechanical observables and unitary operators which, if
implemented in physical systems as measurements and dynamical evolutions, would
contradict the Church-Turing thesis which lies at the foundation of computer
science. We conclude that either the Church-Turing thesis needs revision, or
that only restricted classes of observables may be realized, in principle, as
measurements, and that only restricted classes of unitary operators may be
realized, in principle, as dynamics.

2
The categories of this paper are: math
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn