Tsallis entropy and entanglement constraints in multiqubit systems

We show that the restricted shareability and distribution of multiqubit entanglement can be characterized by Tsallis-$q$ entropy. We first provide a class of bipartite entanglement measures named Tsallis-$q$ entanglement, and provide its analytic formula in two-qubit systems for $1\ensuremath{\leqslant}q\ensuremath{\leqslant}4$. For $2\ensuremath{\leqslant}q\ensuremath{\leqslant}3$, we show a monogamy inequality of multiqubit entanglement in terms of Tsallis-$q$ entanglement, and we also provide a polygamy inequality using Tsallis-$q$ entropy for $1\ensuremath{\leqslant}q\ensuremath{\leqslant}2$ and $3\ensuremath{\leqslant}q\ensuremath{\leqslant}4$.

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