Quantum metrology with two-mode squeezed thermal state: Parity detection and phase sensitivity

Based on the Wigner-function method, we investigate the parity detection and phase sensitivity in a Mach-Zehnder interferometer (MZI) with two-mode squeezed thermal state (TMSTS). Using the classical transformation relation of the MZI, we derive the input-output Wigner functions and then obtain the explicit expressions of parity and phase sensitivity. The results from the numerical calculation show that supersensitivity can be reached only if the input TMSTS have a large number photons.