Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal classical and quantum real and complex dimension witness   We find the minimal number of independent preparations and measurements
certifying the dimension of a classical or quantum system limited to $d$
states, optionally reduced to the real subspace. As a dimension certificate, we
use the linear independence tested by a determinant. We find the sets of
preparations and measurements that maximize the chance to detect larger space
if the extra contribution is very small. We discuss the practical application
of the test to certify the space logical operations on a quantum computer.

32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat