  In order to investigate the role of initial quantum coherence in work
probability distribution, it is necessary to explicitly consider a concrete
measurement apparatus to record work rather than implicitly appealing to
perform an energy measurement. In this paper, we consider a harmonic oscillator
with coherent or squeezing state as measurement apparatus, and propose a
unified framework of quantum work statistics for arbitrary initial state. We
find that work is proportional to the change of the real part of coherent state
parameter, i.e., quantum work can be estimated by the coherent state parameter.
The resulting work probability distribution includes the initial quantum
coherence, and can be reduced to result of traditional two projective energy
measurement scheme (TPM) by squeezing the state of the harmonic oscillator. As
an application, we consider a driven two-level system and investigate the
effects of driving velocity on work statistics. We find that only when the
driving velocity matches the transition frequency of the system can initial
quantum coherence play an important role.
