We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
18/2024
Parameterized coherence measure
Meng-Li Guo, Zhi-Xiang Jin, Jin-Min Liang, Bo Li and Shao-Ming Fei
Abstract
Quantifying coherence is an essential endeavor for both quantum mechanical foundations and quantum technologies. We present a bona fide measure of quantum coherence by utilizing the Tsallis relative operator $(\alpha, \beta)$-entropy. We first prove that the proposed coherence measure fulfills all the criteria of a well defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. We then study the ordering of the Tsallis relative operator $(\alpha, \beta)$-entropy of coherence, Tsallis relative $\alpha$-entropies of coherence, Rényi $\alpha$-entropy of coherence and $l_{1}$ norm of coherence for both pure and mixed qubit states.
This provides a new method for defining new coherence measure and entanglement measure, and also provides a new idea for further study of quantum coherence.
