Quantum uncertainty relations of Tsallis relative α entropy coherence based on MUBs

In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.

Quantum uncertainty relations of Tsallis relative α entropy coherence based on MUBs

In this paper, we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases. For $alpha in left[tfrac{1}{2},1right)cup (1,2]$, the upper and lower bounds of sums of coherence are obtained. However, the above results cannot be verified directly for any $alpha in left(0,tfrac{1}{2}right)$. Hence, we only consider the special case of $alpha =tfrac{1}{n+1}$, where n is a positive integer, and we obtain the upper and lower bounds. By comparing the upper and lower bounds, we find that the upper bound is equal to the lower bound for the special $alpha =tfrac{1}{2}$, and the differences between the upper and the lower bounds will increase as α increases. Furthermore, we discuss the tendency of the sum of coherence, and find that it has the same tendency with respect to the different θ or φ, which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.