Figure 1

Eigenvalues of the matrix $G$ (2) truncated at $N_{\mathrm{tr}}=15$. The simulated measurement was done at $N_p$ $\gamma$ points equidistantly distributed in regions: (a) and (b) $\mathrm{Re}(\gamma )\in [-2,2]$, $\mathrm{Im}(\gamma )\in [-2,2]$; (c) $\mathrm{Re}(\gamma )\in [-1,1]$, $\mathrm{Im}(\gamma )=0$; (d) $\mathrm{Re}(\gamma )\in [1,1.01]$, $\mathrm{Im}(\gamma )=0$. In all panels, 10 equidistant values of the detector efficiency were chosen from the interval $\eta \in [0.1,0.9]$.Reuse & Permissions

Figure 2

A reconstruction of the state (10) according to procedure (5). The following measurements were used: $\mathrm{Re}(\gamma )=-0.2,-0.1,0,0.1,0.2$; $\mathrm{Im}(\gamma )=0.1,-0.5,0,0.5,0.1$; 20 equidistantly distributed detector efficiencies in the interval $[0.1,0.9]$ were used; the Hilbert space was truncated at $N_{\mathrm{tr}}=5$. Panel (a) shows the eigenvalues of the matrix $G$. Panels (b) and (d) show the real and imaginary parts of the reconstructed matrix (in Fock basis). They were obtained using ${10}^6$ iteration of the EM algorithm. Panel (c) shows the variances of the real part ($n\le m$) and imaginary part ($n>m$) of the reconstructed elements given by Eq. (9).Reuse & Permissions

Figure 3

A reconstruction of the signal coherent state $\alpha =\exp \{i\pi /4\}$. (a) The reconstructed Wigner function; (b) the diagonal elements of the reconstructed density matrix; (c) the difference between the exact and the reconstructed Wigner functions; (d) the variance $\sigma (\gamma ,{\gamma }^{*})$. The Wigner function was reconstructed pointwise at 2500 points of the phase plane from $N_r={10}^4$ measurements per point using $N_{\mathrm{it}}={10}^3$ iterations of the EM algorithm. The Hilbert space was truncated at $N_{\mathrm{tr}}=12$; 30 different values of detector efficiencies were used equidistantly distributed in the interval $[0.1,0.9]$.Reuse & Permissions