Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The strong converse exponent of discriminating infinite-dimensional
  quantum states   The sandwiched R\'enyi divergences of two finite-dimensional density
operators quantify their asymptotic distinguishability in the strong converse
domain. This establishes the sandwiched R\'enyi divergences as the
operationally relevant ones among the infinitely many quantum extensions of the
classical R\'enyi divergences for R\'enyi parameter $\alpha>1$. The known proof
of this goes by showing that the sandwiched R\'enyi divergence coincides with
the regularized measured R\'enyi divergence, which in turn is proved by
asymptotic pinching, a fundamentally finite-dimensional technique. Thus, while
the notion of the sandwiched R\'enyi divergences was extended recently to
density operators on an infinite-dimensional Hilbert space (in fact, even for
states of an arbitrary von Neumann algebra), these quantities were so far
lacking an operational interpretation similar to the finite-dimensional case,
and it has also been open whether they coincide with the regularized measured
R\'enyi divergences. In this paper we fill this gap by answering both questions
in the positive for density operators on an infinite-dimensional Hilbert space,
using a simple finite-dimensional approximation technique.
  We also initiate the study of the sandwiched R\'enyi divergences, and the
related problems of the strong converse exponent, for pairs of positive
semi-definite operators that are not necessarily trace-class (this corresponds
to considering weights in a general von Neumann algebra setting). While this
problem does not have an immediate operational relevance, it might be
interesting from the purely mathematical point of view of extending the concept
of R\'enyi (and other) divergences to settings beyond the standard one of
positive trace-class operators (positive normal functionals in the von Neumann
algebra case). We also discuss the R\'enyi $(\alpha,z)$-divergences in this
setting.

23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con