Tighter constraints of multiqubit entanglement for negativity

TL;DR

This paper introduces new, tighter monogamy and polygamy inequalities for multiqubit entanglement based on negativity measures, expanding the understanding of quantum entanglement distribution constraints.

Contribution

It develops a novel class of inequalities for multiqubit entanglement using SCREN and SCRENoA, improving upon existing bounds with tighter constraints.

Findings

Derived new monogamy inequalities for $ ext{SCREN}$ and $ ext{SCRENoA}$.

Established polygamy inequalities valid for different $ ext{alpha}$ ranges.

Demonstrated these inequalities are tighter than previous bounds.

Abstract

We provide a characterization of multiqubit entanglement monogamy and polygamy constraints in terms of negativity. Using the square of convex-roof extended negativity (SCREN) and the Hamming weight of the binary vector related to the distribution of subsystems proposed in Kim (Phys Rev A 97: 012334, 2018), we provide a new class of monogamy inequalities of multiqubit entanglement based on the $\alpha$th power of SCREN for $\alpha\geq1$ and polygamy inequalities for $0\leq\alpha\leq1$ in terms of squared convex-roof extended negativity of assistance (SCRENoA). For the case $\alpha<0$, we give the corresponding polygamy and monogamy relations for SCREN and SCRENoA, respectively. We also show that these new inequalities give rise to tighter constraints than the existing ones.