Hamming weight and tight constraints of multi-qubit entanglement in terms of unified entropy

Abstract

We establish a characterization of multi-qubit entanglement constraints in terms of non-negative power of entanglement measures based on unified-$(q,s)$ entropy. Using the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of tight monogamy inequalities of multi-qubit entanglement based on the $\alpha$th-power of unified-$(q,s)$ entanglement for $\alpha \geq 1$. For $0 \leq \beta \leq 1$, we establish a class of tight polygamy inequalities of multi-qubit entanglement in terms of the $\beta$th-power of unified-$(q,s)$ entanglement of assistance. Thus our results characterize the monogamy and polygamy of multi-qubit entanglement for the full range of non-negative power of unified entanglement.