  Weak measurement [1,19] combined with quantum delayed-choice experiment that
use quantum beam splitter instead of the beam splitter give rise to a
surprising amplification effect, i.e., counterintuitive negative amplification
effect. We show that this effect is caused by the wave and particle behaviours
of the system to be and can't be explained by a semiclassical wave theory, due
to the entanglement of the system and the ancilla in quantum beam splitter. The
amplification mechanism about wave-particle duality in quantum mechanics lead
us to a scheme for implementation of weak measurement in optomechanical system.
