Quantum coherence in mutually unbiased bases

We investigate the l(1) norm of coherence of quantum states in mutually unbiased bases. We find that the sum of squared l(1) norm of coherence of single qubit mixed state is less than two. We derive that the l(1) norms of coherence of three classes of X states in nontrivial mutually unbiased bases for 4-dimensional Hilbert space are equal. We propose the concept of "autotensor of mutually unbiased basis (AMUB)" by the tensor of mutually unbiased bases and depict the level surface of the constant sum of the l(1) norm of coherence of Bell-diagonal states in AMUB. We find that the l(1) norms of coherence of Werner states and isotropic states in AMUB are equal, respectively.