Quantum process tomography with Heisenberg scaling based on Gaussian state and binary detection

We propose a quantum process tomography scheme that utilizes two-mode squeezed vacuum to realize the parameter estimation with Heisenberg scaling. The objective is to estimate a rotating angle of polarization and parity detection is used as the detection strategy. With the help of symplectic matrix theory, we discuss the estimation visibility and sensitivity of output signal in lossless situation, the quantum Fisher information is also given via calculation. Finally, the impacts of two realistic factors on both visibility and sensitivity are also considered, including photon loss during the input generation, and photon loss along with thermal noise during the output detection.