Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An uncertainty view on complementarity and a complementarity view on
  uncertainty   Since the uncertainty about an observable of a system prepared in a quantum
state is usually described by its variance, when the state is mixed, the
variance is a hybrid of quantum and classical uncertainties. Besides that,
complementarity relations are saturated only for pure, single-quanton, quantum
states. For mixed states, the wave-particle quantifiers never saturate the
complementarity relation and can even reach zero for a maximally mixed state.
So, to fully characterize a quanton it is not sufficient to consider its
wave-particle aspect; one has also to regard its correlations with other
systems. In this paper, we discuss the relation between quantum correlations
and local classical uncertainty measures, as well as the relation between
quantum coherence and quantum uncertainty quantifiers. We obtain a complete
complementarity relation for quantum uncertainty, classical uncertainty, and
predictability. The total quantum uncertainty of a d-paths interferometer is
shown to be equivalent to the Wigner-Yanase coherence and the corresponding
classical uncertainty is shown to be a quantum correlation quantifier. The
duality between complementarity and uncertainty is used to derive quantum
correlations measures that complete the complementarity relations for
$l_1$-norm and $l_2$-norm coherences. Besides, we show that Brukner-Zeilinger's
invariant information quantifies both the wave and particle characters of a
quanton and we obtain a sum uncertainty relation for the generalized Gell
Mann's matrices.

2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga