Postselection-Loophole-Free Bell Violation with Genuine Time-Bin Entanglement

Entanglement is an invaluable resource for fundamental tests of physics and the implementation of quantum information protocols such as device-independent secure communications. In particular, time-bin entanglement is widely exploited to reach these purposes both in free space and optical fiber propagation, due to the robustness and simplicity of its implementation. However, all existing realizations of time-bin entanglement suffer from an intrinsic postselection loophole, which undermines their usefulness. Here, we report the first experimental violation of Bell’s inequality with “genuine” time-bin entanglement, free of the postselection loophole. We introduced a novel function of the interferometers at the two measurement stations, that operate as fast synchronized optical switches. This scheme allowed us to obtain a postselection-loophole-free Bell violation of more than 9 standard deviations. Since our scheme is fully implementable using standard fiber-based components and is compatible with modern integrated photonics, our results pave the way for the distribution of genuine time-bin entanglement over long distances.

Figure 1

Bell tests with time-bin entanglement. (a) In the passive TB, by postselecting the events detected in coincidence in the central time slot, Alice and Bob can violate a Bell inequality, but the scheme is affected by the PSL. (b) In the active TB, the passive beam splitter is replaced by a balanced MZI acting as an optical switch, and a PSL-free Bell violation is obtained by exploiting the phase modulator ${\phi }_M$ to not discard any data.

Figure 2

Functioning of the active TB scheme. (a) In a balanced MZI, the relative phase ${\phi }_M$ sensed by a traveling pulse determines the output port at which it will exit with probabilities ${\cos }^2({\phi }_M/2)$ and ${\sin }^2({\phi }_M/2)$. A fast modulator imposes different phase shifts ${\phi }_S$ and ${\phi }_L$ to the $|S⟩$ and $|L⟩$ photons while they are traveling along the balanced MZI. (b) The detection pattern depends on ${\phi }_S$ and ${\phi }_L={\phi }_S-\pi$. If ${\phi }_S=\pi$, all detections occur in the central time slot; if ${\phi }_S=0$, they appear only in the lateral time slots. Any other detection histogram can be obtained with two different ${\phi }_S$ values, one with ${\phi }_S<\pi$ (red dot) and the other with ${\phi }_S>\pi$ (blue dot).

Figure 3

Experimental setup. Bob’s measurement station is analogue to Alice’s. APD: analog photodetector; DM: dichroic mirror; HWP: half waveplate; and QWP: quarter waveplate.

Figure 4

Raw detection histograms obtained with one detector for the passive TB (grey curve) and with the active TB (red curve). The counts are normalized to fairly compare the two histograms.