Bell-Type Test of Energy-Time Entangled Qutrits

We have performed a Bell-type test for energy-time entangled qutrits. A method of inferring the Bell violation in terms of an associated interference visibility is derived. Using this scheme we obtained a Bell value of $2.784\pm 0.023$, representing a violation of $34\sigma$ above the limit for local variables. The scheme has been developed for use at telecom wavelengths and using proven long distance quantum communication architecture to optimize the utility of this high dimensional entanglement resource.

Figure 1

Alice and Bob share entangled (energy time at 1300 nm) qutrits. Measurements are determined via variations in the path lengths of their interferometers. There are five peaks in the arrival time histogram (shown on the right) due to different path combinations. Coincidence detection events in the central peak project onto one of three orthogonal entangled qutrit states. These coincidences (shown on the left) vary as a function of Alice and Bob's phase vectors.

Figure 2

The relationship between the mixing parameter $\lambda$ and the visibility for various dimensions. Also shown are the critical values for $\lambda$ (*) to violate the Bell inequality.

Figure 3

Raw coincidence count rates, circles, as the phases are varied under the Bell phase constraint. Also shown is a fit using Eq. (5) and the noise level. Inset: the three (net) orthogonal results.