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

TL;DR

This paper develops tight monogamy and polygamy inequalities for multi-qubit entanglement using unified entropy measures, revealing comprehensive entanglement constraints based on Hamming weight and power parameters.

Contribution

It introduces a unified framework for entanglement constraints in multi-qubit systems using unified-$(q,s)$ entropy and Hamming weight, covering full non-negative power ranges.

Findings

Established tight monogamy inequalities for $eta extgreater= 0$.

Derived polygamy inequalities for $0 extless= eta extless= 1$.

Characterized full-range entanglement constraints in multi-qubit systems.

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.