Figure 1

Photograph of lithium iodate crystal $\left({\mathrm{LiIO}}_3\right)$ frequency-angular spectrum taken with the helium cadmium laser pump operated at $325\mathrm{nm}$. The angle between the optical axis of the crystal and the laser pump is $59.22°$. Dashed lines select the part of the spectrum (frequency degenerate, collinear regime of SPDC) that contributes to biphoton-based qutrits. Vertical lines at the bottom belong to the spectrum of neon gas which serves as a frequency reference.Reuse & Permissions

Figure 2

Nondegenerate regime of SPDC. The angle between the crystal optical axis and the laser pump is $58.97°$. Dashed lines select the part of the spectrum contributed to ququarts.Reuse & Permissions

Figure 3

Preparation of states ${\Psi }_I$. A nonlinear crystal generates one of the basic ququart state(s) via type-I SPDC. Then the state is transformed by the wave plate QP with the parameters depending on its orientation angle $\alpha$.Reuse & Permissions

Figure 4

Preparation of states ${\Psi }_{II}$. Two nonlinear crystals generate a pair of the basic ququart states via type-I SPDC. The relative phase between states ${\phi }_{14}$ is controlled by two quartz plates QP1, QP2. The basic state amplitudes are controlled with the help of the half-wave plate.Reuse & Permissions

Figure 5

Measurement block for Protocol 1. Brown-Twiss scheme for measuring the intensity correlation between two polarization modes. After the spatial separation at the nonpolarizing 50/50 beam-splitter (NPBS), signal $\left({\lambda }_2\right)$ and idler $\left({\lambda }_1\right)$ photons propagate through the quarter- (QWP1,2) and half- HWP1,2 -wave plates, polarizing prisms (PP1,2) placed in both channels. The interference filter centered at ${\lambda }_1$ (IF) placed in the upper arm selects one frequency mode of a ququart. Finally, photons are registered by detectors (D1,2). The coincidence rate at the output of the coincidence circuit (CC) is proportional to the fourth moment in the field $⟨R⟩$.Reuse & Permissions

Figure 6

Measurement block for Protocol 2. After the input state is subjected to the transformations by wave plates (QP1, QP2), the projective measurements selecting vertical polarizations of ququart components are performed.Reuse & Permissions

Figure 7

Dependence of the coincidence rate on tilting angle $\theta$.Reuse & Permissions

Figure 8

Setup for preparation and measurement of ququarts which can be used in QKD. Wave plates DP1, DP2 oriented at $45°$ with respect to the vertical axis serve as the dichroic retardation plate with variable optical thickness which is controlled by tilting angle $\theta$. Two zero-order plates ZP1, ZP2 allow one to choose the basis.Reuse & Permissions

Figure 9

Dependence of single counts (upper) and coincidences rates (lower) on tilting angle $\theta$.Reuse & Permissions

Figure 10

Measurement part at Bob’s station.Reuse & Permissions