  Quantum coherence characterizes the non-classical feature of a single party
system with respect to a local basis. Based on a recently introduced resource
framework, coherence can be regarded as a resource and be systematically
manipulated and quantified. Operationally, considering the projective
measurement of the state in the computational basis, coherence quantifies the
intrinsic randomness of the measurement outcome conditioned on all the other
quantum systems. However, such a relation is only proven when randomness is
characterized by the Von-Neumann entropy. In this work, we consider several
recently proposed coherence measures and relate them to the general
uncertainties of the projective measurement outcome conditioned on all the
other systems. Our work thus provides a unified framework for redefining
several coherence measures via general conditional entropies. Based on the
relation, we numerically calculate the coherence measures via semi-definite
programming. Furthermore, we discuss the operational meaning of the unified
definition. Our result highlights the close relation between single partite
coherence and bipartite quantum correlation.
