Phase estimation in a multimode nonlienar interferometer.

Simultaneous estimation of multiple phase shifts is very important in quantum metrology as it has implications for the single-shot quantum imaging. Multiparameter estimation has been already demonstrated in linear optics even though its performance is greatly limited by computational difficulty associated with matrix permanent. Here, we propose a scheme that uses nonlinear optical parametric amplification (OPA) to estimate multiple simultaneous phase shifts. The performance of our scheme is compared with the SNL and the Heisenberg limit (HL). We choose homodyne as the measurement strategy in our scheme. As photon loss is the biggest experimental limitation, we also investigate the effect of photon loss in the phase sensitivity.