Triggered Qutrits for Quantum Communication Protocols

A general protocol in quantum information and communication relies in the ability of producing, transmitting, and reconstructing, in general, qunits. In this Letter we show for the first time the experimental implementation of these three basic steps on a pure state in a three-dimensional space, by means of the orbital angular momentum of the photons. The reconstruction of the qutrit is performed with tomographic techniques and a maximum-likelihood estimation method. For the tomographic reconstruction we used more than 2400 different projections. In this way we also demonstrate that we can perform any transformation in the three-dimensional space.

Figure 1

Effect of a hologram on an initially prepared $|0⟩$ mode. This mode is transformed by means of a horizontally displaced hologram of charge $m=+1$. The resulting state is projected onto the basis states. In this case the modes $|0⟩$ and $|1⟩$ are expected to contribute the most to the transformed state. Asterisks: projection onto the $|0⟩$ mode. Diamonds: projection onto the $|1⟩$ mode. The solid line represents the projection onto the “outer” modes, i.e., those not belonging to the basis (1). This projection is found by subtracting to the total number of events those corresponding to the projection onto the elements of the basis. The two positions of the hologram where the transfer to “outer” modes is maximum are taken as new elements of the basis.

Figure 2

Experimental setup. A $351\mathrm{nm}$ wavelength laser pumps a BBO crystal. The two generated $702\mathrm{nm}$ down-converted photons are sent to Alice and Bob’s detectors, respectively. Before being detected each photon propagates through a set of holograms. Each photon was coupled into single mode fibers and directed to detectors based on avalanche photo diodes operating in the photon counting regime.

Figure 3

Results of quantum state tomography applied to three different remotely prepared states of Bob’s qutrits: (a) $0.68|0⟩+0.71|1⟩-0.14|\mathrm{-}\mathrm{1}⟩$; (b) $0.65|0⟩+0.53\exp (-i0.26\pi )|1⟩+0.55\exp (-i0.6\pi )|\mathrm{-}\mathrm{1}⟩$; (c) $0.58|0⟩+0.58\exp (-i0.05\pi )|1⟩+0.58\exp (-i0.89\pi )|\mathrm{-}\mathrm{1}⟩$. Left and middle panels show real and imaginary parts of the reconstructed density matrices; right panels visualize the absolute values of those elements for better comparison of how large the contributions are of the three basic states. From the results it is shown that Alice can control both the relative amplitudes and phases of the sent states.