Figure 1

(a) Setup for the generation of a polarization-path 4-qubit entangled state. A Type-I nonlinear $\beta$-barium-borate crystal (BBO) is pumped by a vertically polarized uv laser at wavelength ${\lambda }_p$ in a double-pass configuration. This produces nonmaximally entangled polarization states that, through the quarter-wave plates QWP${}_1$ and QWP${}_2$ (QWP${}_1$ and QWP${}_2$ are quarter-wave plates for $2{\lambda }_p$ and ${\lambda }_p$, respectively) and mirror M, can be turned into $|{\phi }^{+}{\left(p\right)\rangle }_{AB}$ (cf. the body of the paper). The four-hole mask selects four longitudinal spatial modes within the emission cone of the BBO crystal. The attenuator $\epsilon$ and the half-wave plates HWP${}_1$ and HWP${}_2$ allow the engineering of the polarization-path entangled state ${|\xi \rangle }_{AB}$. (b) Interferometer needed to perform the trace over the path DOF and generate the states used in our study (BS stands for beam splitter). Quartz plates of various thickness have been used to produce ${\rho }^{\downarrow }{\left(q\right)}_{AB}$ and ${\rho }^W{\left(\epsilon \right)}_{AB}$. We also show the analyzers $D_j(j=A,B)$ needed for QST. Each $D_j$ is made of the cascade of a QWP, an HWP, and a polarizing beam splitter (PBS). The signal then enters a photodetector.Reuse & Permissions

Figure 2

(a) Exploration of the ${\mathcal{D}}^{\leftrightarrow }\text{-vs-}\mathcal{S}$ plane. The solid line shows the MNCMS boundary (b) Experimental comparison between AMID and ${\mathcal{D}}^{\leftrightarrow }$. The solid lines embody the bounds to $\mathcal{A}$ at set values of ${\mathcal{D}}^{\leftrightarrow }$. Both panels show experimental states and associated uncertainties.Reuse & Permissions