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...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.展开更多
Several new series of approximately mutually unbiased bases are constructed by using Gauss sums and Jacobi sums over Galois rings GR(p2, r), and the tensor method.
基金This paper is supported by Startup Foundation for Doctors of Nanchang Hangkong University(No.EA201907210).
文摘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.
基金supported by the Natural Science Foundation of China under Grant No.61370089the Tsinghua National Laboratory for Information Science and Technology+1 种基金by the Fundamental Research Funds for the Central Universities under Grant No.JZ2014HGBZ0349by Science and Technology on Information Assurance Lab.KJ-12-01
文摘Several new series of approximately mutually unbiased bases are constructed by using Gauss sums and Jacobi sums over Galois rings GR(p2, r), and the tensor method.
