Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monogamy relations and upper bounds for the generalized $W$-class states
  using R\'{e}nyi-$\alpha$ entropy   We investigate monogamy relations and upper bounds for generalized $W$-class
states related to the R\'{e}nyi-$\alpha$ entropy. First, we present an
analytical formula on R\'{e}nyi-$\alpha$ entanglement (R$\alpha$E) and
R\'{e}nyi-$\alpha$ entanglement of assistance (REoA) of a reduced density
matrix for a generalized $W$-class states. According to the analytical formula,
we show monogamy and polygamy relations for generalized $W$-class states in
terms of R$\alpha$E and REoA. Then we give the upper bounds for generalized
$W$-class states in terms of R$\alpha$E. Next, we provide tighter monogamy
relations for generalized $W$-class states in terms of concurrence and
convex-roof extended negativity and obtain the monogamy relations for
R$\alpha$E by the analytical expression between R$\alpha$E and concurrence.
Finally, we apply our results into quantum games and present a new bound of the
nonclassicality of quantum games restricting to generalized $W$-class states.

34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat