Experimental realization of polarization qutrits from nonmaximally entangled states

Based on a recent proposal [Phys. Rev. A 71, 062337 (2005)], we have experimentally realized two-photon polarization qutrits by using nonmaximally entangled states and linear optical transformations. By this technique, high-fidelity mutually unbiased qutrits are generated at a high brilliance level.

Figure 1

(Color online) Optical setup for generation and analysis of polarization qutrits. (a) The entanglement source is used to produce the seed state. The reciprocal weights of the ${\mid H⟩}_1{\mid H⟩}_2$ and ${\mid V⟩}_1{\mid V⟩}_2$ components are set by controlling the pump beam polarization in the first passage through the $\beta \text{−}\mathrm{Ba}{\mathrm{B}}_2{\mathrm{O}}_4$ (BBO) by the ${\lambda }_p∕2$ half-wave plate and in the second passage by the ${\lambda }_p∕4$ quarter-wave plate. (b) The qutrit is encoded by applying the $H^{\prime }\otimes H^{\prime }$ transformation by two HWP plates and by proper phase shifts $P_{\alpha }\otimes P_{\alpha }$ performed by QWP plates. (c), Finally the state is characterized by polarization quantum state tomography.

Figure 2

(Color online) Visibility $\left(V\right)$ of nonmaximally entangled state $\mid \chi ⟩$ vs the $\mid HH⟩$ weight $d_H^2$. The black line represents the theoretical curve $V=2\sqrt{d_H^2(1-d_H^2)}$. Error bars are smaller than the point symbols.

Figure 3

(Color online) Experimental quantum tomographies (real parts) of the seed states $\mid {\chi }_1⟩$ and $\mid {\chi }_2⟩$ expressed in the $\{\mid HH⟩,\mid HV⟩,\mid VH⟩,\mid VV⟩\}$ basis. For the two states we obtain the purities ${\mathcal{P}}_{\mid {\chi }_1⟩}=0.908\pm 0.034$ and ${\mathcal{P}}_{\mid {\chi }_2⟩}=0.930\pm 0.036$. The imaginary components are negligible.

Figure 4

(Color online) Experimental quantum tomography (a) and theoretical density matrices (b) of the states $\mid v_1⟩$, $\mid w_3⟩$, and $\mid z_3⟩$. The upper pictures represent the real (Re) parts of the density matrices, while the lower pictures represent the imaginary (Im) parts. We measured the purities ${\mathcal{P}}_{\mid v_1⟩}=0.974\pm 0.030$, ${\mathcal{P}}_{\mid w3⟩}=0.904\pm 0.033$, and ${\mathcal{P}}_{\mid z3⟩}=0.895\pm 0.028$.

Figure 5

(Color online) Experimental quantum tomography (a) and theoretical density matrices (b) of the states $\mid w_1⟩$ and $\mid w_2⟩$. We have the purities ${\mathcal{P}}_{\mid w_1⟩}=0.969\pm 0.030$ and ${\mathcal{P}}_{\mid w_2⟩}=0.918\pm 0.024$.

Figure 6

(Color online) Experimental quantum tomography (a) and theoretical density matrices (b) of the states $\mid z_1⟩$ and $\mid z_2⟩$. We have the purities ${\mathcal{P}}_{\mid z_1⟩}=0.931\pm 0.028$ and ${\mathcal{P}}_{\mid z2⟩}=0.937\pm 0.032$.