Complete Deterministic Linear Optics Bell State Analysis

We show how hyperentanglement allows us to deterministically distinguish between all four polarization Bell states of two photons. In this proof-of-principle experiment, we employ the intrinsic time-energy correlation of photon pairs generated with high temporal definition in addition to the polarization entanglement obtained from parametric down-conversion. For the identification, no nonlinear optical elements or auxiliary photons are needed. The new possibilities this complete Bell measurement offers are demonstrated by realizing an optimal dense coding protocol.

Figure 1

Setup for a complete Bell state analysis (see text).

Figure 2

Hong-Ou-Mandel interference on a beam splitter for all four Bell states. Experimental results (symbols) and fitted curves of the coincidence count rates as a function of the path length difference between the BBO crystal and the beam splitter for the two photons, corresponding to the time delay of the photons arriving at the beam splitter. The visibilities of the curves are between 92.4% and 95.3%.

Figure 3

Coincidence rate between detectors D2 and D4 as a function of the path length difference between the two interferometer arms. This corresponds to the relative phase between orthogonal polarizations, when preparing either $|{\Phi }^{+}⟩$ or $|{\Phi }^{-}⟩$ at the input of the BSA.

Figure 4

Results of the complete Bell state analysis showing the relative detection probability for the various Bell states.