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 α entropy 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 α entropy. It proves that this family of quantifiers satisfy all the standard criteria and particularly cover several typical coherence measures.
Highlights
Quantification of coherence is the most essential ingredient in the quantum theory and in the practical application
We establish a family of coherence measures that are closely related to the Tsallis relative α entropy
We prove that these coherence measures satisfy all the required criteria for a satisfactory coherence measure especially including the strong monotonicity
Summary
The coherence and the Tsallis relative α entropy. The resource theory includes three ingredients: the free states, the resource states and the free operations[24,46]. In the practical experiment, it is not necessary for us to erase any information This means that the incoherent operation {Kn} can increase the coherence, which violates the fundamental spirit of a resource theory. Ref.[22] found that the coherence based on the Tsallis relative α entropy is such a coherence quantifier without the strong monotonicity. The coherence measures based on the Tsallis relative α entropy. Cα(ρ) defines a family of coherence measures related to the Tsallis relative α entropy. The l2 norm has been revived for coherence measure by considering the square root of the density matrices This is much like the quantification of quantum correlation proposed in ref.[50]. We would like to compare our coherence measure with other analytic coherence measures, that is, the measure based on l1 norm, the relative entropy and the skew information.
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