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# Monogamy relations and upper bounds for the generalized $$W$$-class states using R\'{e}nyi-$$\alpha$$ entropy

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### 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.

### Author and article information

###### Journal
30 April 2020
###### Article
2010.16311