  We study quantum phase sensing with an asymmetric two-mode entangled coherent
state (ECS) in which the two local amplitudes have different values. We find
the phenomenon of the asymmetry-enhanced phase sensing which the asymmetry can
significantly increase the precise of the phase estimation. We further study
the effect of decoherence induced by the photon loss on quantum phase sensing.
It is shown that the asymmetric ECSs have stronger capability against
decoherence over the symmetric ECSs. It is indicated that the asymmetric ECSs
have obvious advantages over the symmetric ECSs in the quantum phase sensing.
We also study the practical phase sensing scheme with the intensity-difference
measurement, and show that the asymmetry in the asymmetric ECSs can enhance the
phase sensitivity in the practical phase measurement scheme. Our work reveals
the asymmetry in the asymmetric ECSs is a new quantum-sensing resource, and
opens a new way to the ultra-sensitive quantum phase sensing in the presence of
photon losses.
