Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On quantum non-signalling boxes   A classical non-signalling (or causal) box is an operation on classical
bipartite input with classical bipartite output such that no signal can be sent
from a party to the other through the use of the box. The quantum counterpart
of such boxes, i.e. completely positive trace-preserving maps on bipartite
states, though studied in literature, have been investigated less intensively
than classical boxes. We present here some results and remarks about such maps.
In particular, we analyze: the relations among properties as causality,
non-locality and entanglement; the connection between causal and entanglement
breaking maps; the characterization of causal maps in terms of the
classification of states with fixed reductions. We also provide new proofs of
the fact that every non-product unitary transformation is not causal, as well
as for the equivalence of the so-called semicausality and semilocalizability
properties.

17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci