Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The best approximation of an objective state with a given set of quantum
  states   Approximating a quantum state by the convex mixing of some given states has
strong experimental significance and provides potential applications in quantum
resource theory. Here we find a closed form of the minimal distance in the
sense of l_2 norm between a given d-dimensional objective quantum state and the
state convexly mixed by those restricted in any given (mixed-) state set. In
particular, we present the minimal number of the states in the given set to
achieve the optimal distance. The validity of our closed solution is further
verified numerically by several randomly generated quantum states.

4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph