Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operational applications of the diamond norm and related measures in
  quantifying the non-physicality of quantum maps   Although quantum channels underlie the dynamics of quantum states, maps which
are not physical channels -- that is, not completely positive -- can often be
encountered in settings such as entanglement detection, non-Markovian quantum
dynamics, or error mitigation. We introduce an operational approach to the
quantitative study of the non-physicality of linear maps based on different
ways to approximate a given linear map with quantum channels. Our first measure
directly quantifies the cost of simulating a given map using physically
implementable quantum channels, shifting the difficulty in simulating
unphysical dynamics onto the task of simulating linear combinations of quantum
states. Our second measure benchmarks the quantitative advantages that a
non-completely-positive map can provide in discrimination-based quantum games.
Notably, we show that for any trace-preserving map, the quantities both reduce
to a fundamental distance measure: the diamond norm, thus endowing this norm
with new operational meanings in the characterisation of linear maps. We
discuss applications of our results to structural physical approximations of
positive maps, quantification of non-Markovianity, and bounding the cost of
error mitigation.

25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org