Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of mutually unbiased maximally entangled bases in
  $\mathbb{C}^{2^s}\otimes\mathbb{C}^{2^s}$ by using Galois rings   Mutually unbiased bases plays a central role in quantum mechanics and quantum
information processing. As an important class of mutually unbiased bases,
mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have
attracted much attention in recent years. In the paper, we try to construct
MUMEBs in $\mathbb{C}^{2^s} \otimes \mathbb{C}^{2^s}$ by using Galois rings,
which is different from the work in \cite{xu2}, where finite fields are used.
As applications, we obtain several new types of MUMEBs in
$\mathbb{C}^{2^s}\otimes\mathbb{C}^{2^s}$ and prove that $M(2^s,2^s)\geq
3(2^s-1)$, which raises the lower bound of $M(2^s,2^s)$ given in \cite{xu}.

28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph