Lower Bound on the Speed of Nonlocal Correlations without Locality and Measurement Choice Loopholes

In their well-known paper, Einstein, Podolsky, and Rosen called the nonlocal correlation in quantum entanglement a “spooky action at a distance.” If the spooky action does exist, what is its speed? All previous experiments along this direction have locality and freedom-of-choice loopholes. Here, we strictly closed the loopholes by observing a 12 h continuous violation of the Bell inequality and concluded that the lower bound speed of spooky action was 4 orders of magnitude of the speed of light if Earth’s speed in any inertial reference frame was less than ${10}^{-3}$ time the speed of light.

Figure 1

Diagram of experimental setup for testing the speed of spooky action. (a) Birds-eye view of the experiment. We generated entangled photon pairs in the sending point and utilized an integrated sending system to distribute them into two east-west oriented receiving points $A$ and $B$. Receiving site $A$ used an off-axis reflection telescope with 400 mm diameter, and $B$ used a refraction telescope with 127 mm diameter. Both receiving sites $A$ and $B$ had polarization analyzing units (the orange box). (b) Entanglement generation setup. A pair of 45° mirrors and a dual-wavelength PBS formed the Sagnac interferometer. A 22.5° dual-wavelength HWP was used to swap the horizontal and vertical polarization. The DM was used to distinguish the pump light and the signal light. The entangled photons were coupled to SMFs through aspherical lens. (c) Active polarization analyzing unit in receiving site A. A HWP, an EOM, a PBS, and two multimode fiber-coupled single photon counting modules (SPCMs) constitute an active polarization analyzing unit. A quantum random number generator (QRNG) and an amplifier were used to drive the EOM. The signals from the SPCMs combined with the logic module were sent to a time digital converter (TDC). (d) Active polarization analyzing unit in receiving site $B$.

Figure 2

Space-time diagrams of the speed measurement experiment. Points $A$ and $B$ indicated measurement events at sites $A$ and $B$, respectively. Points $a$ and $b$ indicated $A$ and $B$’s setting choice. Point $E$ represented the entanglement generation. $X(Y)$ was the intersections of the $E$ future light cone and the $A(B)$ past-light cone. Points $A^{\prime }$ and $B^{\prime }$ indicated the closest events belonging to $X$ and $Y$, respectively.

Figure 3

Twelve-hour continuous experimental data for the CHSH inequality violation. Each blue data point represents the value of $S$ in one time interval $T$, 1800 sec in our experiment. The red line represents the classical limit. According to the picture, all 26 data points violated the Bell-CHSH inequality by 1–10 standard deviations above the local realistic bound of 2, depending on weather conditions. In order to reduce the daylight noise, we implemented experiments from 7 pm to 7 am of the next morning.

Figure 4

The speed of spooky action at different $\beta$ and $\theta$. For any $\beta$, the speed’s lower bound has a minimum when $\theta$ was $\pi /2$. And as long as $\beta <1$, i.e., Earth’s center speed was less than the speed of light, the speed of spooky action was beyond the speed of light.