Tighter superadditivity relations for $l_{1}$-norm coherence measure

TL;DR

This paper derives tighter superadditivity inequalities for the $l_1$-norm coherence measure in multiqubit quantum systems, improving understanding of coherence distribution with novel relations for higher powers.

Contribution

It introduces new, tighter superadditivity inequalities for the $l_1$-norm coherence measure applicable to multiqubit states, especially involving the $eta$-th power for $eta eq 1$.

Findings

New superadditivity inequalities are tighter than existing ones.

Relations are established for the $eta$-th power of $l_1$-norm coherence with $eta eq 1$.

Results are supported by detailed examples.

Abstract

Quantum coherence serves as a crucial physical resource, with its quantification emerging as a focal point in contemporary research. Superadditivity constitutes one of the most fundamental attributes in characterizing the coherence distribution in multipartite quantum systems. In this paper, we provide a way to derive tighter superadditivity inequalities of $l_1$-norm coherence measure for arbitrary multiqubit states. We present a category of superadditivity relations related to the $\alpha$-th ($\alpha\geqslant 2$) power of $l_{1}$-norm coherence $C_{l_{1}}$ under certain conditions. Our results are better than existing ones and are illustrated in detail with examples.