Quantum dense metrology by an SU(2)-in-SU(1,1) nested interferometer

With the help of quantum entanglement, quantum dense metrology (QDM) is a technique that can make 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 (SUIs) can realize QDM with detection loss tolerance but is limited in absolute sensitivity. Here, we present a QDM scheme with a linear or SU(2) interferometer nested inside an SUI. By using a degenerate SUI and controlling the phase angle of the phase-sensitive amplifiers in the SUI, we can achieve the optimum quantum enhancement in the measurement precision of an arbitrary mixture of phase and amplitude modulation.