Quantum Coherence of Qubit States with respect to Mutually Unbiased Bases

We study the coherence of qubit states with respect to any set of mutually unbiased bases (MUBs), in terms of the l(1) norm of coherence, the modified trace norm of coherence and the geometry measure of coherence. We present the arbitrary expressions of a complete set of MUBs in C-2 and the forms of any qubit states under these complete sets of MUBs. Then we calculate coherence of qubit states with respect to any complete sets of MUBs based on different coherence measures. It is shown that the sum of the coherence or the squared coherence is upper or lower bounded. We derive analytically these bounds and establish tight relations between quantum coherence and mutually unbiased bases.