Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of Heisenberg's error-disturbance relation   While the slogan "no measurement without disturbance" has established itself
under the name Heisenberg effect in the consciousness of the scientifically
interested public, a precise statement of this fundamental feature of the
quantum world has remained elusive, and serious attempts at rigorous
formulations of it as a consequence of quantum theory have led to seemingly
conflicting preliminary results. Here we show that despite recent claims to the
contrary [Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)], Heisenberg-type
inequalities can be proven that describe a trade-off between the precision of a
position measurement and the necessary resulting disturbance of momentum (and
vice versa). More generally, these inequalities are instances of an uncertainty
relation for the imprecisions of any joint measurement of position and
momentum. Measures of error and disturbance are here defined as figures of
merit characteristic of measuring devices. As such they are state independent,
each giving worst-case estimates across all states, in contrast to previous
work that is concerned with the relationship between error and disturbance in
an individual state.

10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci