Though a well-verified approach of quantifying quantum coherence is l1-norm, this is not normalized for a multi-qubit (multi-level) system. We propose a modification to show that the altered expression normalizes a multi-qubit (multi-level) system coherence with numerical studies.
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 [Formula: see text]-norm coherence measure for arbitrary multiqubit states. We present a category of superadditivity relations related to the [Formula: see text]th [Formula: see text] power of [Formula: see text]-norm coherence [Formula: see text] under certain conditions. Our results are better than the existing ones and are illustrated in detail with examples.
Abstract Since a rigorous framework for quantifying quantum coherence was established by Baumgratz et al (2014 Phys. Rev. Lett. 113 140401), many coherence measures have been found. For a given coherence measure C , extending the values of C on pure states to mixed states by the convex roof construction, we will get a valid coherence measure C ¯ , we call C ¯ the corresponding convex roof quantifier of C . Whether C = C ¯ for a given coherence measure is an important question. In this work, we show that for the widely used coherence measure, l 1 norm of coherence C l 1 , it holds that C l 1 ≠ C l 1 ¯ .