  Kirkwood-Dirac (KD) quasiprobability is a quantum analog of phase space
probability of classical statistical mechanics, allowing negative or/and
nonreal values. It gives an informationally complete representation of a
quantum state. Recent works have revealed the important roles played by the KD
quasiprobability in the broad fields of quantum science and quantum technology.
In the present work, we use the KD quasiprobability to access the quantum
coherence in a quantum state. We show that the $l_1$-norm of the imaginary part
of the KD quasiprobability over an incoherent reference basis and a second
basis, maximized over all possible choices of the latter, can be used to
quantify quantum coherence, satisfying certain desirable properties. It is
upper bounded by the quantum uncertainty, i.e., the quantum standard deviation,
of the incoherent basis in the state. It gives a lower bound to the $l_1$-norm
quantum coherence, and for a single qubit, they are identical. We discuss the
measurement of the KD coherence based on the measurement of the KD
quasiprobability and an optimization procedure in hybrid quantum-classical
schemes, and suggest statistical interpretations. We also discuss its relevance
in the physics of linear response regime.
