Tighter Constraints of Multipartite Systems in terms of General Quantum Correlations

TL;DR

This paper derives tighter monogamy and polygamy inequalities for general quantum correlations in multipartite systems using Hamming weight, improving upon existing bounds and demonstrated with concurrence and Tsallis-$q$ entanglement.

Contribution

It introduces new, tighter monogamy and polygamy inequalities for quantum correlations based on Hamming weight, extending previous bounds.

Findings

Derived inequalities are tighter than previous ones.

Applicable to measures like concurrence and Tsallis-$q$ entanglement.

Showed advantages of new inequalities through examples.

Abstract

Monogamy and polygamy relations characterize the quantum correlation distributions among multipartite quantum systems. We investigate the monogamy and polygamy relations satisfied by measures of general quantum correlation. By using the Hamming weight, we derive new monogamy and polygamy inequalities satisfied by the $\beta$-th power and the $\alpha$-th power of general quantum correlations, respectively. We show that these monogamy and polygamy relations are tighter than the existing ones, such as [Int. J. Theor. Phys. 60, 1455-1470 (2021)]. Taking concurrence and the Tsallis-$q$ entanglement of assistance as examples, we show the advantages of our results.