The quantum uncertainty relation for skew information of coherence

Abstract The quantum uncertainty relation characterizes the restriction of the quantum coherence on different measurement bases. The skew information of coherence is a coherence measure both operationally and informatically. We study the quantum uncertainty relation for the skew information of coherence under any two orthonormal bases. In qubit and qutrit systems, we derive the quantum uncertainty relations with the lower bounds in the factorized forms by the purity of quantum states and the incompatibility between two orthonormal bases. Especially the lower bound in qubit systems is strictly positive for non-maximally mixed states and incompatible orthonormal bases. These quantum uncertainty relations reveal the intrinsic relation among the coherence, the purity and the incompatibility between two orthonormal bases quantitatively. The advantages of these quantum uncertainty relations are illustrated by some specific examples. This method we developed here is beneficial to some other quantum uncertainty relations.