The Tsallis Relative 2-Entropy of Coherence under Mutually Unbiased Bases

The performance of quantum coherence under different bases is an important subject in quantum theory and quantum information science. This paper mainly focuses on the Tsallis relative 2-entropy of coherence of quantum states under mutually unbiased bases(MUBs) in two, three and four dimensional systems. For single-qubit mixed states, the sum under complete MUBs is less than v6; for Gisin states and Bell-diagonal states in four dimensional system, the sum under a new set of "autotensor of mutually unbiased basis" (AMUBs) is less than nine. For three classes of X states in three-dimensional system, each Tsallis relative 2-entropy of coherence under nontrivial unbiased bases is found equal. Also the surfaces of the sum of the Tsallis relative 2-entropy of coherence under MUBs and AMUBs are described, respectively. Among them, a surface of a special class of X states in AMUBs is an ellipsoid.