Remedying the strong monotonicity of the coherence measure in terms of the Tsallis relative $\alpha$ entropy

TL;DR

This paper introduces a family of coherence measures based on Tsallis relative alpha entropy that satisfy all standard criteria, including strong monotonicity, addressing previous limitations.

Contribution

It develops a new family of coherence quantifiers related to Tsallis entropy that meet all standard criteria, especially strong monotonicity.

Findings

The new measures satisfy all standard coherence criteria.

They include several well-known coherence measures as special cases.

The measures successfully address the violation of strong monotonicity.

Abstract

Coherence is the most fundamental quantum feature of the nonclassical systems. The understanding of coherence within the resource theory has been attracting increasing interest among which the quantification of coherence is an essential ingredient. A satisfactory measure should meet certain standard criteria. It seems that the most crucial criterion should be the strong monotonicity, that is, average coherence doesn't increase under the (sub-selective) incoherent operations. Recently, the Tsallis relative $\alpha $ entropy [A. E. Rastegin, Phys. Rev. A \textbf{93}, 032136 (2016)] has been tried to quantify the coherence. But it was shown to violate the strong monotonicity, even though it can unambiguously distinguish the coherent and the incoherent states with the monotonicity. Here we establish a family of coherence quantifiers which are closely related to the Tsallis relative $\alpha $ entropy. It proves that this family of quantifiers satisfy all the standard criteria and particularly cover several typical coherence measures.