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

Li Heng-Mei^{1, †,}, Xu Xue-Xiang², Yuan Hong-Chun^{3, 4}, Wang Zhen¹

A lossless Mach–Zehner interferometer with TMSTS as inputs. The modes are labeled by the annihilation operators a_i, b_i for the input port and a_f, b_f for the final output ports, respectively. BS₁ and BS₂ are 50:50 beam splitters. At the output of the MZI, a parity measurement on mode a_f is implemented.