Long-distance distribution of genuine energy-time entanglement

Abstract

Any practical realization of entanglement-based quantum communication must be intrinsically secure and able to span long distances avoiding the need of a straight line between the communicating parties. The violation of Bell's inequality offers a method for the certification of quantum links without knowing the inner workings of the devices. Energy-time entanglement quantum communication satisfies all these requirements. However, currently there is a fundamental obstacle with the standard configuration adopted: an intrinsic geometrical loophole that can be exploited to break the security of the communication, in addition to other loopholes. Here we show the first experimental Bell violation with energy-time entanglement distributed over 1 km of optical fibres that is free of this geometrical loophole. This is achieved by adopting a new experimental design, and by using an actively stabilized fibre-based long interferometer. Our results represent an important step towards long-distance secure quantum communication in optical fibres.

Figure 1. Energy-time Bell test configurations.

(a) Typical fibre-based implementation of Franson’s scheme. (b) Fibre-based version of the hug configuration. (c) Experimental setup used for implementing the hug configuration with a long fibre-based interferometer. Photon pairs generated in a non-linear crystal are sent through two cross-linked unbalanced Mach–Zehnder interferometers at Alice and Bob’s sites. An optical delay line is used to set the indistinguishability between the short–short and long–long two-photon paths (see the main text for details). The long interferometer comprises a 1-km long telecom single-mode fibre spool in each arm. An extra 40 m of optical fibre is added in the S_B arm by the fibre stretcher, which is then balanced by an equal amount of fibre in the other arm. The total arm length in this interferometer is then 1.04 km. The long–short path length difference in both interferometers is 2 m of optical fibres.

Figure 2. Net coincident counts versus the delay line position.

Two-photon interference pattern is observed in case (a) with the stabilization system active, whereas (b) shows a second measurement over the same range of the delay line with stabilization turned off. The error bars shows the s.d. assuming a poissonian distribution for the photon statistics.

Figure 3. Coincidence interference curves and Bell CHSH inequality violation.

Graphs (a–d) show the normalized coincidence detections across Alice and Bob’s detectors without accidental subtraction. (a) and (b) correspond to the cases where φ_b=0 and (c) and (d) to the cases where φ_b=π/2. Integration time for each data point is 1 s with an average rate of ≈100 coincidences counts. The rate of single counts is ≈74,000 and 54,000 detections per second for each detector of Alice and Bob, respectively. The curves are obtained varying the phase difference φ_a in Alice’s interferometer with the moving mirror, while actively keeping fixed the relative phase φ_b. (e) Shows the measured value for each probability correlation function (E) appearing in the Bell CHSH inequality. Solid black lines show the maximum possible value for each function E. The corresponding experimental Bell violation yields S=2.39±0.12. The difference between the fit curve and the data points in (a–d) is due to random drifts in the piezo movement and the statistical distribution of the single-photon detections. The error bars shows the s.d. assuming a poissonian distribution for the photon statistics.