  With the help of quantum entanglement, quantum dense metrology (QDM) is a
technique that can perform the joint estimates of two conjugate quantities such
as phase and amplitude modulations of an optical field with an accuracy beating
the standard quantum limit simultaneously. SU(1,1) interferometers (SUI) can
realize QDM with detection loss tolerance but is limited in absolute
sensitivity. Here we present a QDM scheme with a linear interferometer (SU(2))
nested inside an SU(1,1) interferometer. By using a degenerate SUI and
controlling the phase angle of the phase-sensitive amplifers in SUI, we can
achieve the optimum quantum enhancement in the measurement precision of
arbitrary mixture of phase and amplitude modulation.
