Estimation of the Wigner distribution of single-mode Gaussian states: A comparative study

Enhanced Phase Estimation in Parity‐Detection‐Based Mach–Zehnder Interferometer using Non‐Gaussian Two‐Mode Squeezed Thermal Input State

“…To this end, we make use of the following two facts: (i) Both modes of the TMSV state independently interacting with lossy channels ( Figure 1 a) is equivalent to the case of two single‐mode squeezed vacuum states interacting with independent lossy channels followed by a 50:50 beam splitter (Figure 1b) [ 67 ] and (ii) The TMST state (11) can be generated by mixing two single‐mode squeezed thermal state using a 50:50 beam splitter. The covariance matrix for a single‐mode squeezed vacuum state interacting with a lossy channel is $$$$\begin{equation} V_{r_0,\eta } = \frac{1}{2}\def\eqcellsep{&}\begin{pmatrix} \eta e^{-2r_0} +1-\eta & 0 \\ 0& \eta e^{2r_0} +1-\eta \end{pmatrix}.$$…”