Monogamy relations and upper bounds for the generalized $W$-class states
using R\'{e}nyi-$\alpha$ entropy
- URL: http://arxiv.org/abs/2010.16311v1
- Date: Thu, 30 Apr 2020 09:27:40 GMT
- Title: Monogamy relations and upper bounds for the generalized $W$-class states
using R\'{e}nyi-$\alpha$ entropy
- Authors: Yanying Liang, Zhu-Jun Zheng, Chuan-Jie Zhu
- Abstract summary: We investigate monogamy relations and upper bounds for generalized $W$-class states related to the R'enyi-$alpha$ entropy.
We apply our results into quantum games and present a new bound of the nonclassicality of quantum games restricting to generalized $W$-class states.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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