Observation of Stronger-than-Binary Correlations with Entangled Photonic Qutrits

We present the first experimental confirmation of the quantum-mechanical prediction of stronger-than-binary correlations. These are correlations that cannot be explained under the assumption that the occurrence of a particular outcome of an $n\ge 3$-outcome measurement is due to a two-step process in which, in the first step, some classical mechanism precludes $n-2$ of the outcomes and, in the second step, a binary measurement generates the outcome. Our experiment uses pairs of photonic qutrits distributed between two laboratories, where randomly chosen three-outcome measurements are performed. We report a violation by 9.3 standard deviations of the optimal inequality for nonsignaling binary correlations.

Figure 1

Two possible explanations for the measurement process. Suppose a measurement with three possible outcomes represented by red, green, and blue lights. The process that generates the final outcome (represented by the blue light flashing) can be either (a) a sequence of two steps: (1) The red outcome is precluded by a classical mechanism (e.g., the initial position of the measured system). (2) A general two-outcome measurement selects between the two remaining outcomes. Or (b), the measurement is genuinely ternary in the sense that it cannot be explained as in (a).

Figure 2

Experimental setup. The source of pairs of photons and the first measurement party, Alice, are in laboratory Lab1, while the second measurement party, Bob, is in laboratory Lab2. The distance between Alice’s and Bob’s measurement setups is approximately 8 m. The pump laser is a continuous wave laser of 404 nm wavelength and 100 mW power. Subsequently, beam displacers are used to construct phase-stable interferometers. The beam displacers introduce a 4.21 mm displacement of the vertically polarized component; beam displacer BD1 operates at 404 nm and is approximately 36.41 mm long, beam displacers BD2–BD5 operate at 404 nm and are approximately 39.70 mm long. The pump beam is separated into two paths by means of the half wave plates HWP1–HWP3 and BD1, where the fast axis of HWP1 is oriented at 15° with respect to the horizontal axis, HWP2 is oriented at 27.37°, and HWP3 at 0°. After BD1 and HWP1–HWP3, the pump state is $(\sqrt{2}|V_u⟩+|H_u⟩-|V_l⟩)/2$, where $H$ ($V$) stands for horizontal (vertical) polarization and $u$ ($l$) denotes the upper (lower) path. The two paths of the pump beam are then focused on two spots of two 0.5 mm thick type-I cut $\beta$-borate crystals (BBO) to generate the spatial mode and polarization mode hybrid entangled two-photon state $|\psi ⟩$; see Eq. (7). The local measurement setting 0, see Eq. (8), and 1, see Eq. (9), for Alice and Bob are constructed using the polarizing beam splitters PBS1 and PBS2, the half wave plates HWP4–HWP13, and BD2–BD4. The orientations of HWP4–HWP13 depend on the measurement setting and are chosen according to Table 1. HWP4, HWP8, HWP9, and HWP13 are mounted in electric rotators to switch the measurement settings automatically and the random number generators Quantis-USB-4M (ID Quantique) are used to locally select the measurement basis. Six fiber coupled single photon detectors D1–D6 are used to detect the photons. Interference filters with a bandwidth of 3 nm are used before each detector to remove background photon noise (not shown). Coincidences between D1–D3 and D4–D6 are detected with the coincidence logic ID800 (ID Quantique, not shown), using a coincidence window of 3.2 ns.