Experimental Entangled Entanglement

All previous tests of local realism have studied correlations between single-particle measurements. In the present experiment, we have performed a Bell experiment on three particles in which one of the measurements corresponds to a projection onto a maximally entangled state. We show theoretically and experimentally that correlations between these entangled measurements and single-particle measurements are too strong for any local-realistic theory and are experimentally exploited to violate a Clauser-Horne-Shimony-Holt-Bell inequality by more than 5 standard deviations. We refer to this possibility as “entangled entanglement.”

Figure 1

Schematic cartoon for the Bell experiment based on an entangled entangled state. (a) A source emits the entangled three-photon state $|{\Phi }^{-}{⟩}_{a,b}=\frac{1}{\sqrt{2}}(|H{⟩}_a|{\varphi }^{-}{⟩}_{b_1,b_2}-|V{⟩}_a|{\psi }^{+}{⟩}_{b_1,b_2})$, where one photon is received by Alice and the two other photons by Bob. Alice makes polarization measurements on her photon. If the photon’s polarization is measured to be parallel (perpendicular) to the orientation ${\theta }_1$ of the analyzer, the measurement outcome is $+1$ ($-1$). In contrast, Bob makes projective measurements onto a two-particle entangled state, where the orientation of his analyzer is defined by the angle ${\theta }_2$. Bob’s outcomes are also defined as $+1$ or $-1$. (b) For the local settings ${\theta }_1+{\theta }_2=0$, $\pi$, $2\pi$, etc., they observe perfect correlations; i.e., the product of their local measurement outcomes yields $+1$. (c) Perfect anticorrelations will be obtained when ${\theta }_1+{\theta }_2=\pi /2$, $3\pi /2$, etc., given by the product $-1$ of the local results.

Figure 2

Setup for the experimental realization. A spontaneous parametric down-conversion source emits $|{\varphi }^{+}⟩$ states, into both pair of modes $a1$ and $b1$ and $a2$ and $b2$. Comp is a 1 mm thick BBO crystal used to compensate the walk-off in the down-conversion crystal [15]. The modes $a1$ and $a2$ are superposed at the polarizing beam splitter PBS1. In our case, the PBS transmits horizontally polarized and reflects vertically polarized photons. Each mode $T$, $a$, $b1$, $b2$ passes through a QWP. Projecting the trigger qubit $T$ onto the state $|H{⟩}_T$, we generate the state $|{\Phi }^{-}{⟩}_{a,b}=\frac{1}{\sqrt{2}}(|H{⟩}_a|{\varphi }^{-}{⟩}_{b_1,b_2}-|V{⟩}_a|{\psi }^{+}{⟩}_{b_1,b_2})$. The photon in mode $a$ is sent to Alice, who makes single-photon polarization measurements, determined by the orientation angle ${\theta }_1$ of her linear polarizer. The photons in mode $b1$ and $b2$ belong to Bob, who uses a modified Bell-state analyzer to make projective measurements onto a coherent superposition of $|{\varphi }^{-}{⟩}_{b_1,b_2}$ and $|{\psi }^{+}{⟩}_{b_1,b_2}$, where the mixing angle ${\theta }_2$ is determined by the angle ${\theta }_2/2$, of the HWP in mode $b2$.

Figure 3

Measured coincidence fringes for the entangled entangled state. Bob’s half-wave plate was initially set to 0° and made projective measurements onto the state $|{\varphi }^{-}{⟩}_{b_1,b_2}$. The total number of fourfold coincidence counts measured in 1800 seconds as a function of the angle of Alice’s polarizer is shown as solid squares. Fitting the curve to a sinusoid (solid line) yields a visibility of $(78\pm 2)\%$. After changing Bob’s measurement setting to project onto the state $\frac{1}{\sqrt{2}}(|{\varphi }^{-}{⟩}_{b_1,b_2}+|{\psi }^{+}{⟩}_{b_1,b_2})$, the procedure was repeated. The data for these settings are shown as open circles. The sinusoidal fit (dotted line) yields a visibility of $(83\pm 2)\%$.

Figure 4

Experimentally measured coincidence counting rates used to test the CHSH-Bell inequality. The requisite coincidence measurements for the 16 different measurement settings are shown. Each measurement was performed for 1800 seconds. For measurement settings ${\theta }_1$ and ${\theta }_2$, the axis labels $++$, $+-$, $-+$, and $--$ refer to the actual settings of $({\theta }_1,{\theta }_1)$, $({\theta }_1,{\theta }_2+\pi /2)$, $({\theta }_1+\pi /2,{\theta }_2)$, and $({\theta }_1+\pi /2,{\theta }_2+\pi /2)$, respectively. These data yielded the Bell parameter $S=2.48\pm 0.09$, which is in conflict with local realism by over 5 standard deviations.