Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Private quantum codes: introduction and connection with higher rank
  numerical ranges   We give a brief introduction to private quantum codes, a basic notion in
quantum cryptography and key distribution. Private code states are
characterized by indistinguishability of their output states under the action
of a quantum channel, and we show that higher rank numerical ranges can be used
to describe them. We also show how this description arises naturally via
conjugate channels and the bridge between quantum error correction and
cryptography.

27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom